A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation

Abstract

In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem.

Keywords

• Stochastic potential-KdV equation
• Symmetries
• Optimal system
• Similarity reductions
• Nonlinear self adjoint
• Conservation laws