Abstract
Abstract Two types of linear inhomogeneous integral equations, which yield solutions of a broad class of nonlinear evolution equations, are investigated. One type is characterized by a two-fold integration with an arbitrary measure and contour over a complex variable k , and thier complex conjugates, whereas the other one has a two-fold integration over one and the same contour. The inhomogeneous term, which may contain an arbitrary function of k , makes it possible to define a matrix structure on the solutions of the integral equations. The elements of these matrices are shown to obey a system of partial differential equations, the special form of which depends on the choice of the dispersion relation occurring in the integral equations. For special elements of the matrices closed partial differential equations can be derived, such as e.g. the nonlinear Schrodinger equation and the (real and complex) modified Korteweg-de Vries and sine-Gordon equations. The relations between the matrix elements are shown to lead to Miura transformations between the various partial differential equations.
Sign-in/Register to access full text options 
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 callMore From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
