Interaction solutions for supersymmetric mKdV-B equation

Abstract

The N = 1 supersymmetric mKdV-B system is transformed to a system of coupled bosonic equations by using the bosonization approach. The bosonized supersymmetric mKdV-B (BSmKdV-B) equation includes the usual mKdV equation and a linear partial differential equation. The bosonization approach can thus effectively avoid difficulties caused by anticommutative fermionic fields of the supersymmetric systems. The consistent tanh expansion (CTE) method is applied to the BSmKdV-B equation. A nonauto-Bäcklund (BT) theorem is obtained by using CTE method. The interaction solutions among solitons and other complicated waves including Painlevé II waves and periodic cnoidal waves are given through a nonauto-BT theorem. The features of the soliton-cnoidal interaction solutions are investigated both in analytical and graphical ways by combining the mapping and deformation method.

Soliton molecules, nonlocal symmetry and CRE method of the KdV equation with higher-order corrections

“…The CRE or the consistent tanh expansion (CTE) method can be applied to find these types of solutions [52]. The method has been applied to various nonlinear systems, including to the classical integrable nonlinear equations [53], the supersymmetric integrable systems [54] and the non-integrable nonlinear equation [55]. The method can also test the integrable property of the nonlinear systems.…”

Soliton molecules and the CRE method in the extended mKdV equation

“…The consistent Riccati expansion (CRE) or the consistent tanh expansion (CTE) method can be applied to find these types of solutions [21]. The method has been applied to various nonlinear systems, including the modified Kadomtsev-Petviashvili (KP) equation [22], the modified KdV-Calogero-Bogoyavlenkskii-Schiff equation [23], the supersymmetric integrable systems [24] and the nonintegrable cubic generalised KP equation [25]. In this paper, the main purpose of our work is to construct soliton molecules, interaction between a soliton molecule and one-soliton, and interaction between solitons and cnoidal periodic wave solutions for an extended modified KdV (mKdV) equation.…”