Using Hirota’s bilinear derivative method to derive single-breather solutions for the modified nonlinear Schrödinger(MNLS)equation and the derivative nonlinear Schrödinger(DNLS)equation under non-vanishing ...Using Hirota’s bilinear derivative method to derive single-breather solutions for the modified nonlinear Schrödinger(MNLS)equation and the derivative nonlinear Schrödinger(DNLS)equation under non-vanishing boundary conditions,along with explicit mixed solutions combining breather-type and pure solitons.The collision dynamics between pure and breather-type solitons in a mixed solution has been graphically demonstrated and ana-lyzed.Furthermore,by setting specific parameter to zero,we naturally ob-tain corresponding single-breather solution and its explicit mixed solutions with pure solitons for the DNLS equation.The mixed soliton solution can asymptotically degenerate into a simple algebraic summation of a simple pure soliton and a breather in the infinite past or the infinite future,which was graphically validated.展开更多
The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous b...The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.展开更多
文摘Using Hirota’s bilinear derivative method to derive single-breather solutions for the modified nonlinear Schrödinger(MNLS)equation and the derivative nonlinear Schrödinger(DNLS)equation under non-vanishing boundary conditions,along with explicit mixed solutions combining breather-type and pure solitons.The collision dynamics between pure and breather-type solitons in a mixed solution has been graphically demonstrated and ana-lyzed.Furthermore,by setting specific parameter to zero,we naturally ob-tain corresponding single-breather solution and its explicit mixed solutions with pure solitons for the DNLS equation.The mixed soliton solution can asymptotically degenerate into a simple algebraic summation of a simple pure soliton and a breather in the infinite past or the infinite future,which was graphically validated.
文摘The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.
