New homoclinic orbits and soliton solutions for the classical Boussinesq equations;

Because solitary waves are firmly connected with homoclinic orbits, we then prove, by geometric singular perturbation method, that the perburbed system has a homoclinic orbit.

An existence theorem concerning denumerable 1-homoclinic orbits and countable families of 1-periodic orbits was given under a generic condition; and an intuitionistic description about those orbits was also given.

The existence and relevant theorems of Homoclinic orbits for another generalized Lienard system are obtained.

This dissertation mainly concerns with the existence of homoclinic orbits and subharmonics for a class of p-Laplace difference equations by using the critical point theory.

One of multiple modes of the governing equation was obtained using Galerkin s method to obtain a parametrically excited(caused by temperature) Duffing s oscillator,and the fixed points and homoclinic orbits .

In consequence,the homoclinic orbit disappeared,i.

Based on it,the homoclinic orbits with different parameters at the equilibrium O and P~+ are searched.

Global attractor and homoclinic orbits for Ginzberg-Landau equations;

Homoclinic Orbits for the Zakharov System and Hirota Equation;

In recent years there have been existence studies on the extensive of homoclinic orbits for nearly dissipative PDEs,which are closely related to chaos.

The existence of positive homoclinic orbits is obtained by the variational approach for a class of the second order differential equations-α(x)u+β(x)u2+γ(x)u3=0,where the coefficient functions α(x),β(x),γ(x) satisfy xα′(x)≥0,xβ′(x)≤0,xγ′(x)≤0 for all x∈R.

The second section is concerned with the number of zeros of the Abelian integrals for a cubic Hamiltonian system with double homoclinic orbit under 2n + 1 .