Affiliation:
1. Samarkand State University
2. Urgench State University
Abstract
In this paper, we consider the Cauchy problem for the non-stationary modified Korteweg–de Vries equation with an additional term and a self-consistent source in the case of moving eigenvalues. Also, the evolution of the scattering data of the Dirac operator is obtained, the potential of which is the solution of the loaded modified Korteweg–de Vries equation with a self-consistent source in the class of rapidly decreasing functions. Specific examples are given to illustrate the application of the obtained results.
Subject
General Medicine,Linguistics and Language,Language and Linguistics,Education,General Decision Sciences,Public Health, Environmental and Occupational Health,Orthopedics and Sports Medicine,Physical Therapy, Sports Therapy and Rehabilitation,Education,General Medicine,General Medicine,General Physics and Astronomy,Cell Biology,Plant Science,Molecular Biology,Biochemistry,Biotechnology