Application of scaling invariance approach, P-test and soliton solutions for couple of dynamical models

Abstract

In the current article, we will apply the scaling invariance technique to find conservation laws (CLs) for the nonlinear Chiral Schrödinger equation (NLCSE) with variable coefficients and the (2+1)-dimensional Maccari system. In addition to the establishment of CLs for these models, we will also look for diverse forms of dromions (solitons) solutions in polynomial forms such as optical solitary and soliton wave with Jacobi elliptic solutions. These solutions will be obtained by applying a well known and renowned integration scheme known as the unified scheme (US). Moreover, the solvability of these governing models is investigated by means of a much blooming algorithm, which is known as the Painlevé algorithm.

Keywords

• 35A20
• Analytic methods
• 35L05
• Wave equation
• 35Q51
• Solitons