High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation

Backlund Transformation and N-soliton-like Solutions to the Combined KdV-Burgers Equation with Variable Coefficients

Abstract: In this paper, through a new transformation, the combined KdvBurgers equation with variable coefficients(vcKdvB) is reduced to a new simplified equation.Based on the homogeneous balance principle(HBP),we studied the Backlund transformation(BT) and several exact soliton-like solutions to this vcKdvB equation. Including single kink-like solitary wave solutions, double-soliton-like solut...

Higher-order integrable evolution equation and its soliton solutions

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. We demonstrate its integrability, provide its Lax pair, and, applying the Darboux transfromation, present its first and second order soliton solutions. The equation and its solutions have two free parameters. Setting one of these parameters to zero...

New explicit solutions of the fifth-order KdV equation with variable coefficients

By means of the modified CK’s direct method, we give out the relationship between variable coefficients of the fifth-order KdV equation and the corresponding constant coefficient ones. At the same time, we have studied the generalized fifth-order KdV equation with constants coefficients using the Lie symmetry group methods. By applying the nonclassical symmetry method we found that the analyzed...

Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

Multiple Soliton Solutions of Second-order Benjamin-ono Equation

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of Multiple soliton solutions of secondorder Benjamin-Ono equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.