Year: 1994
Type: article
Abstract: The solution u(t,x,y) of the Kadomtsev-Petviashvili I (KPI) equation with given initial data u(0,x,y) belonging to the Schwartz space is considered. No additional special constraints, usually considered in the literature, such as integral dx u(0,x,y)=0 are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that u(t,x,y) satisfies a special evolution version of the KPI equation and that, in general, delta t u(t,x,y) has different left and right limits at the initial time t=0. The conditions of the type integral dx u(t,x,y)=0, integral dx xu y (t,x,y)=0 and so on (first, second, etc. 'constraints') are dynamically generated by the evolution equation for t not=0. On the other hand integral dx integral dy u(t,x,y) with prescribed order of integrations is not necessarily equal to zero and gives a non-trivial integral of motion.
Source: Inverse Problems
Authors: M Boiti, F Pempinelli, A Pogrebkov
Institution: University of Salento
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2086901797