Exact Kink Solutions Research Articles

(Invited) Kink solutions of the complex cubic– quintic Ginzburg-Landau equation in the presence of intrapulse Raman scattering

We present a study of solutions of the complex cubic–quintic Ginzburg-Landau equation (CCQGLE) and CCQGLE perturbed with the term responsible for the intrapulse Raman scattering (IRS). In both cases, using the method of first-order autonomous sub-equations, novel exact kink and antikink solutions have been identified. These solutions are represented in explicit analytic form. The numerical investigation of the influence of the IRS on the shape, amplitude, and velocity of the right side of the observed "front" CCQGLE solution revealed a good correlation with the identical features predicted by the newly discovered exact kink solution.

New exact kink solutions and periodic form solutions for a generalized Zakharov–Kuznetsov equation with variable coefficients

In this short letter, with the aid of symbolic computational system Mathematic, new exact solutions including kink solutions, soliton-like solutions and periodic form solutions for a generalized Zakharov–Kuznetsov equation with variable coefficients are obtained using the generalized Riccati equation mapping method.

New exact kink solutions, solitons and periodic form solutions for a combined KdV and Schwarzian KdV equation

In this short letter, new exact solutions including kink solutions, soliton-like solutions and periodic form solutions for a combined version of the potential KdV equation and the Schwarzian KdV equation are obtained using the generalized Riccati equation mapping method.

Class of deformable double-well potentials with exact kink solutions

We present a class of nonlinear double-well potentials, whose shapes can be varied in several different manners as a function of a parameter. Families of exact kink solutions associated with each potential of the class are found, and the dependence of their energies upon the potential parameter is also discussed.

Exact kink solutions in a new non-linear hyperbolic double-well potential

The authors propose a model of a kink bearing Hamiltonian with a new non-linear potential V( phi , mu ) whose double-well shape can be varied continuously as a function of the parameter mu and which has the phi 4 potential as a particular case. Exact classical kink solutions that depend on mu are obtained. The rest masses and rest energies of the kinks are also determined.