Asymptotic soliton-like solutions to the Benjamin–Bona–Mahony equation with variable coefficients and a strong singularity

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...

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients

Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.

Asymptotic behavior of initially "large and smooth" pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrödinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Th...