The paper deals with a problem of asymptotic soliton-like solutions to the Benjamin-Bona-Mahony (BBM) equation with a small parameter at the highest derivative and variable coefficients depending on the variables x, t as well as a small parameter. An algorithm for constructing solutions to the BBM equation has been proposed and theorems on accuracy of such solutions have been proved. Mathematics Subject Classification (2010): 35C20; 35Q53; 35B25

No abstract

The paper deals with the problem of the existence of solutions to an inhomogeneous linear differential equation of higher even order. The problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type. The theorem on necessary and sufficient conditions of the existence of solutions to the differential equation in the Schwartz space of rapidly decreasing functions is proved by means of theory of pseudodifferential operators.

There is studied problem on existence of solutions to nonhomogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type.By means of Fourier transform and theory of pseudodifferential operators there is proved the theorem on necessary and sufficient conditions on existence of solutions to linear non-homogeneous differential equation of higher even order in the Schwartz space.