The theory of chaos and shadowing developed recently by the author is amplified to the case of a heteroclinically tubular cycle. Specifically, let F be a C3 diffeomorphism on a Banach space. F has a heteroclinically tubular cycle that connects two normally hyperbolic invariant manifolds. Around the heteroclinically tubular cycle, a Bernoulli shift dynamics of submanifolds is established through...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...

We establish the existence of homoclinic orbits for the near{integrable double discrete sine-Gordon (dDSG) equation under periodic boundary conditions. The hyperbolic structure and homoclinic orbits are constructed through the B acklund transformation and Lax pair. A geometric perturbation method based on Mel'nikov analysis is used to establish necessary criteria for the persistent of temporal...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

The aim of this paper is to investigate the stability problem for the Pexider type (hyperbolic) trigonometric functional equation f(x + y) + f(x + σy) = λg(x)h(y) under the conditions : |f(x + y) + f(x + σy)− λg(x)h(y)| ≤ φ(x), φ(y), and min{φ(x), φ(y)}. As a consequence, we have generalized the results of stability for the cosine(d’Alembert), sine, and the Wilson functional equations by J. Bak...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

This paper outlines a study into the exact solutions of (2+1)-dimensional Heisenberg ferromagnetic spin chain equation that is used to illustrate materials magnetic ordering by applying two recent techniques, namely, Sardar-subequation method and extended rational sine–cosine sinh–cosh methods. Abundant such as bright soliton, dark combined bright–dark singular soliton other periodic wave expre...

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎