‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solito...

In this paper we consider the relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations. We observe that canonical Hamiltonian equations can be obtained by variational principle from an action functional and consider invariance properties of this functional as it is done in Lagrangian formalism. We rewrite the well–kno...

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one–parameter Hamiltonian symmetries admitted by the PDEs [1]. The same result holds for semidiscrete Hamiltonian equations [2]. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for...

Recently, a quantum version of Painlevé equations from the point of view of their symmetries was proposed by H. Nagoya. These quantum Painlevé equations can be written as Hamiltonian systems with a (noncommutative) polynomial Hamiltonian HJ. We give a characterization of the quantum Painlevé equations by certain holomorphic properties. Namely, we introduce canonical transformations such that th...

Hamiltonian system LetA ⊆ R be an open set andH :A×R×R → R be a smooth function (A×R is called the phase space). Consider the system of ordinary differential equations q̇k = ∂H(q, p, t)/∂pk, ṗk = −∂H(q, p, t)/∂qk, for k = 1, . . . , d. The equations are called Hamilton equations, and H is called a Hamiltonian function. A dynamical system described by Hamilton equations is called a Hamiltonian sy...

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canoni-cal Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange form...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...