Fundamental solution of degenerated Fokker - Planck equation
Fundamental solution of degenerated Fokker - Planck equation is built by means of the Fourier transform method. The result is checked by direct calculation.
Nonlinear Sciences
Nonlinear Sciences
All posts under tag "Nonlinear Sciences"
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Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
Mathematics
MATH-PH
HEP-TH
Nonlinear Sciences
Note on the 2-component Analogue of 2-dimensional Long Wave-Short Wave Resonance Interaction System
An integrable two-component analogue of the two-dimensional long wave-short wave resonance interaction (2c-2d-LSRI) system is studied. Wronskian solutions of 2c-2d-LSRI system are presented. A reduced case, which describes resonant interaction between an interfacial wave and two surface wave packets
System
Nonlinear Sciences
A closed-form solution in a dynamical system related to Bianchi IX
The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painleve' function.
System
Nonlinear Sciences
A supersymmetric Sawada-Kotera equation
A new supersymmetric equation is proposed for the Sawada-Kotera equation. The integrability of this equation is shown by the existence of Lax representation and infinite conserved quantities and a recursion operator.
Nonlinear Sciences
Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm
Chaotic systems have been broadly exploited through the last two decades to build encryption methods. Recently, two new image encryption schemes have been proposed, where the encryption process involves a permutation operation and an XOR-like transformation of the shuffled pixels, which are controll
Computer Science
Multimedia
Analysis
Nonlinear Sciences
Cryptography and Security
Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane
The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians $H_k$, $k=1$, 2, 3,..., on a plane. The elements of the dihedral group $D_{2
Mathematics
Quantum Physics
Nonlinear Sciences
MATH-PH
System
HEP-TH
Integrals of open 2D lattices
We present an explicit formula for integrals of the open 2D Toda lattice of type $A_n$. This formula is applicable for various reductions of this lattice. To illustrate the concept we find integrals of the Toda $G_2$ lattice. We also reveal a connection between the open Toda $A_n$ and Shabat-Yamilov
Nonlinear Sciences
Lattice representation and dark solitons of the Fokas-Lenells equation
This work is devoted to an integrable generalization of the nonlinear Schr'odinger equation proposed by Fokas and Lenells. I discuss the relationships between this equation and other integrable models. Using the reduction of the Fokas-Lenells equation to the already known ones I obtain the N-dark so
Nonlinear Sciences
q-Analogue of Shock Soliton Solution
By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and
Nonlinear Sciences
q-oscillator from the q-Hermite Polynomial
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-os
Mathematics
Quantum Physics
Nonlinear Sciences
MATH-PH
HEP-TH
Random Sequential Generation of Intervals for the Cascade Model of Food Webs
The cascade model generates a food web at random. In it the species are labeled from 0 to $m$, and arcs are given at random between pairs of the species. For an arc with endpoints $i$ and $j$ ($i<j$), the species $i$ is eaten by the species labeled $j$. The chain length (height), generated at random
Model
Quantitative Biology
Nonlinear Sciences
The essence of the homotopy analysis method
The generalized Taylor expansion including a secret auxiliary parameter $h$ which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of $h$ can't be understood in the frame of the homotopy analysis method. This i
Mathematics
Analysis
Nonlinear Sciences
A new integrable generalization of the Korteweg - de Vries equation
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and ge
Mathematics
MATH-PH
Nonlinear Sciences
A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps
We propose a nonperturbative approach to nonabelian two-form gauge theory. We formulate the theory on a lattice in terms of plaquette as fundamental dynamical variable, and assign U(N) Chan-Paton colors at each boundary link. We show that, on hypercubic lattices, such colored plaquette variables con
HEP-LAT
Nonlinear Sciences
HEP-TH
Condensed Matter
Comodule algebras and integrable systems
A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras, the (classical and quantum) q-oscillator algebra and the Re
Mathematics
MATH-PH
System
Nonlinear Sciences
Existence of periodic solutions for enzyme-catalysed reactions with periodic substrate input
Considering a basic enzyme-catalysed reaction, in which the rate of input of the substrate varies periodically in time, we give a necessary and sufficient condition for the existence of a periodic solution of the reaction equations. The proof employs the Leray-Schauder degree, applied to an appropri
Quantitative Biology
Nonlinear Sciences
Financial rogue waves
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and rela
Quantitative Finance
Nonlinear Sciences
Generalization of the linear r-matrix formulation through Loop coproducts
A new method for the construction of classical integrable systems, that we call loop coproduct formulation, is presented. We show that the linear r-matrix formulation, the Sklyanin algebras and the reflection algebras can be obtained as particular subcases of this framework. We comment on the possib
Nonlinear Sciences
Generalized statistical complexity and Fisher-Renyi entropy product in the $H$-atom
By using the Renyi entropy, and following the same scheme that in the Fisher-Renyi entropy product case, a generalized statistical complexity is defined. Several properties of it, including inequalities and lower and upper bounds are derived. The hydrogen atom is used as a test system where to quant
Physics
Nonlinear Sciences
Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I
The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to
Nonlinear Sciences
Lemniscates do not survive Laplacian growth
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc., is known to be integrable and to exhibit a large number of exact solutions. In this work, the boun
Mathematics
MATH-PH
Condensed Matter
Nonlinear Sciences
New Algebraic Approaches to Classical Boundary Layer Problems
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These parameter functions enable one to find the solutions of some rel
Mathematics
MATH-PH
Nonlinear Sciences
Physics
New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-hamiltonian structure
We study restricted multiple three wave interaction system by the inverse scattering method. We develop the algebraic approach in terms of classical $r$-matrix and give an interpretation of the Poisson brackets as linear $r$-matrix algebra. The solutions are expressed in terms of polynomials of thet
System
Nonlinear Sciences
On the Equations of Nonstationary Transonic Gas Flows
The method of point transformation of the functions and variables for construction of particular solutions of the Equations of Nonstationary Transonic Gas Flows is used.
Nonlinear Sciences
Separation of variables in one partial integrable case of Goryachev
We show that the equations of motion in one partial integrable case of Goryachev in the rigid body dynamics can be separated by the appropriate change of variables, the new variables x, y being hyperelliptic functions of time. The natural phase variables (components of coordinates and momenta) are e
Nonlinear Sciences
Signatures of fractal clustering of aerosols advected under gravity
Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example at the ground lev
Physics
Nonlinear Sciences
Superintegrability on sl(2)-coalgebra spaces
We review a recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions, that can be used to generate 'dynamically' a large family of curved spaces. From an algebraic viewpoint, such spaces are obtained through kinetic energy Hamiltonians
Mathematics
MATH-PH
Nonlinear Sciences
Thirring Model with Jump Defect
The purpose of our work is to extend the formulation of classical affine Toda Models in the presence of jump defects to pure fermionic Thirring model. As a first attempt we construct the Lagrangian of the Grassmanian Thirring model with jump defect (of Backlund type) and present its conserved modifi
Model
Nonlinear Sciences
Boundary effects on energy dissipation in a cellular automaton model
In this paper, we numerically study energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Numerical results show that there is a nonvanishing energy dissipation rate Ed, and no true free-flow phase exists in the deterministic and nondeterm
Nonlinear Sciences
Model
Physics
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve Equation: II
The degenerate third Painleve' equation, $u'(t)=(u'(t))^2/u(t)-u'(t)/t+1/t(-8c u^2(t)+2ab)+b^2/u(t)$, where $c=+/-1$, $b>0$, and $a$ is a complex parameter, is studied via the Isomonodromy Deformation Method. Asymptotics of general regular and singular solutions $u(t)$ as $t -> +/-infty$ and $t -> +
Mathematics
Nonlinear Sciences
Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging method, using a recent development of this theory for perturbed in
Nonlinear Sciences
Integrable Lagrangians and modular forms
We investigate non-degenerate Lagrangians of the form $$ int f(u_x, u_y, u_t) dx dy dt $$ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic reductions. We demonstrate that the integrability condit
Mathematics
HEP-TH
Nonlinear Sciences
Lie conformal algebra cohomology and the variational complex
We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a struct
Mathematics
MATH-PH
Nonlinear Sciences
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at all and thus is more general than the traditional multiple-sca
Mathematics
MATH-PH
Nonlinear Sciences
Physics
On the localized wave patterns supported by convection-reaction-diffusion equation
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values.
Nonlinear Sciences
On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
We consider N=2 supersymmetric extensions of the Camassa-Holm and Hunter-Saxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2-dimensional supercircle. We use the bi-Hamiltonian formulation to derive L
Mathematics
MATH-PH
HEP-TH
Nonlinear Sciences
![Reflection matrices for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model](/images/papers/0809.0421/cover.png)
Reflection matrices for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model
The graded reflection equation is investigated for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model. We have found four classes of diagonal solutions with at the most one free parameter and twelve classes of non-diagonal ones with the number of free parameters depending on the number of bosonic ($r$) and f
Model
HEP-TH
Nonlinear Sciences
Special features of the KdV-Sawada-Kotera equation
The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed KdV equation, the asymptotic expansion of the solution is developed through third order within the framework of a Normal
Nonlinear Sciences
The integrals of motion for the elliptic deformation of the Virasoro and $W_N$ algebra
We review the free field realization of the deformed Virasoro algebra $Vir_{q,t}$ and the deformed $W$ algebra $W_{q,t}(hat{gl_N})$. We explicitly construct two classes of infinitly many commutative operators ${cal I}_m$, ${cal G}_m$, $(m in {mathbb N})$, in terms of these algebras. They can be rega
Nonlinear Sciences
A Class of Mixed Integrable Models
The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the zero curvature representation and some soliton solutions are
Model
HEP-TH
Nonlinear Sciences
Coexistence of Social Norms based on In- and Out-group Interactions
The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed social behavior by way of local interaction converges to a st
Physics
Computer Science
Multiagent Systems
Nonlinear Sciences
Phase transition in a class of non-linear random networks
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity k = 2. Also, we show that both, pairwise correlation
Quantitative Biology
Network
Nonlinear Sciences
Traveling waves and localized structures: An alternative view of nonlinear evolution equations
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other generates structures that are localized in the vicinity of th
Nonlinear Sciences
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525
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1777
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241
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12
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79
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58
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711
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14
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8
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63
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67
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81
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1022
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5
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15
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194
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858
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399
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164
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270