NONLINEAR EQUATIONS WITH INTEGRATED OPERATOR STRUCTURES

Abstract

The article is devoted to the construction of nonlinear equations with partial derivatives possessing Lax operator structure. The presence of Lax pair is supposed to allow to integrate the obtained equations with the help of the inverse scattering problem method. For the equations with partial derivatives having the form of local conservation law one of the possible Lax pairs is given.

Keywords

• закон сохранения
• метод обратной задачи рассеяния
• нелинейные уравнения с частными производными
• пара лакса
• эволюционное уравнение
• the conservation law
• the inverse scattering problem method
• nonlinear equations with partial derivatives
• lax pair
• the evolutionary equation