Anti-kink Wave Solutions Research Articles

Bifurcations of travelling wave solutions in a model of the hydrogen-bonded systems

By using the theory of bifucations of dynamical systems to a model of the Hydrogen-bonded systems, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. In some simple parametric conditions, exact explicit and implicit solution formulas are listed.

A direct truncation method for finding abundant exact solutions and application to the one-dimensional higher-order Schrödinger equation

We suggest a direct truncation technique for finding exact solutions of nonlinear differential equation, this method is based on the WTC test. As an application, abundant new exact stationary solutions of the one-dimensional higher-order nonlinear Schrodinger equation are obtained. These solutions include bright, dark, kink or anti-kink solitary wave solutions, which are dependent of the model and free parameters in the solutions. Algebraic solitary-like solution and new periodic solutions are also obtained. An interesting fact is that some solitary solutions can convert into the periodic solutions and vice versa when the free parameters are changed. (C) 2004 Elsevier Ltd. All rights reserved.

Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation

The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation ( B ( m , n ) equation), u tt − u xx − a ( u n ) xx + b ( u m ) xxxx =0, is studied by using bifurcation theory of dynamical system . As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave , kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given.

Bifurcations of travelling wave solutions for the generalization form of the modified KdV equation

By using the theory of bifurcations of dynamical systems to the generalization form of the modified KdV equation, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.

Travelling wave solutions in a model of the helix polypeptide chains

By using the theory of bifucations of dynamical systems to a model of the helix polypeptide chains, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. In some simple conditions, exact explicit and implicit solution formulas are listed.