Travelling waves solutions of the KP equation in weakly dispersive media
نویسندگان
چکیده
Abstract The current work focuses on the solutions of Kadomtsev and Petviashvili (KP) equation, which models nonlinear waves in a dispersive medium. modified auxiliary equation approach is utilized to find analytical KP equation. Consequently, set including Jacobi elliptic solitary periodic obtained. geometry derived plotted with an appropriate choice parameters. It can be seen that proposed method powerful used solve partial differential equations due its simplicity.
منابع مشابه
Quasi - classical ∂̄ - dressing approach to the weakly dispersive KP hierarchy
Recently proposed quasi-classical ∂̄-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical ∂̄-dressing method to describe dispersive corrections of any order. We show how calculate the ∂̄ problems at any order for a rather general class of integrable systems, presenting explicit results for the KP hierarchy case. We ...
متن کاملGlobal Existence of Solutions to the Fowler Equation in a Neighbourhood of Travelling-Waves
The study of mechanisms that allow the formation of structures such as sand dunes and ripples at the bottom of a fluid flow plays a crucial role in the understanding of coastal dynamics. The modeling of these phenomena is particularly complex since we must not only solve the Navier-Stokes or Saint-Venant equations with equation for sediment transport, but also take into account the evolution of...
متن کاملSoliton Solutions of the Kp Equation and Application to Shallow Water Waves
The main purpose of this paper is to give a survey of recent development on a classification of soliton solutions of the KP equation. The paper is self-contained, and we give a complete proof for the theorems needed for the classification. The classification is based on the Schubert decomposition of the real Grassmann manifold, Gr(N, M), the set of N -dimensional subspaces in RM . Each soliton ...
متن کاملNumerical study of the KP equation for non-periodic waves
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line...
متن کاملThe interaction of long and short waves in dispersive media
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model the interaction of long and short waves is mathematically attractive and such a system has been studied over the last decades. We evaluate the validity of this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Open Physics
سال: 2022
ISSN: ['2391-5471']
DOI: https://doi.org/10.1515/phys-2022-0053