Lax pairs, infinite conservation laws of stochastic potential Korteweg–de Vries equation and their solutions by using Darboux transformation

Abstract

This article carried out the Lax pairs and infinite conservation laws of the stochastic potential Korteweg–de Vries (spKdV) equation, which claims its integrability in the Lax pair sense. The infinite conservation laws of the spKdV equation were established using its Lax pair. The Darboux transformation was conducted and several pertinent theorems and propositions were briefly discussed for deriving especially the complexiton-type solutions. Some complicated efficient solutions, such as higher-order positon, negaton, hybrid positon-rational solution and negaton-rational solutions were explored from the spKdV equation by choosing initial trivial seed solutions.