Abstract
The Wick‐type stochastic KP equation is researched. The stochastic single‐soliton solutions and stochastic multisoliton solutions are shown by using the Hermite transform and Darboux transformation.
Highlights
In recent decades, there has been an increasing interest in taking random effects into account in modeling, analyzing, simulating, and predicting complex phenomena, which have been widely recognized in geophysical and climate dynamics, materials science, chemistry biology, and other areas, see 1, 2
Taking the Hermite transform of 2.2, the Wick product is turned into ordinary products between complex numbers, and the equation takes the form
Using the similar idea of the Darboux transformation about the determinant nonlinear partial differential equations, we can obtain the soliton solutions of 1.2, which can be seen in the following theorem
Summary
There has been an increasing interest in taking random effects into account in modeling, analyzing, simulating, and predicting complex phenomena, which have been widely recognized in geophysical and climate dynamics, materials science, chemistry biology, and other areas, see 1, 2. Abstract and Applied Analysis balance method 4, 5 has been widely applied to derive the nonlinear transformations and exact solutions especially the solitary waves and Darboux transformation 6 , as well as the similar reductions of nonlinear PDEs in mathematical physics. These subjects have been researched by many authors. For SPDEs, in 7 , Holden et al gave white noise functional approach to research stochastic partial differential equations in Wick versions, in which the random effects are taken into account. The Wick-type stochastic KP equation in white noise environment is considered as the following form: Utx f t ♦Uxxx.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
