论文标题
通过gel'fand- levitan-marchenko方程的逆散射方法，用于某些负顺序非线性波方程
Inverse scattering method via Gel'fand--Levitan--Marchenko equation for some negative order nonlinear wave equations
论文作者
论文摘要
A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations.在线性系统成为经典的Zakharov--Shabat系统的情况下，检查了整个轴上的逆散射问题，由两个方程组成，并承认真正的对称和真实的反对称潜力。参考这些结果，非线性klein klein方程的全差异性版本与标量场（CKG）（CKG）和负顺序修改的Korteweg-de Vries（NMKDV）方程的N- soliton解决方案通过gel'fand-levand-levand-levandan-marchan-racko-rackan-racko-racko-rackan-rackan-rackan-racko-rackan-rarkanko-arcarchako-rackankoarkan-rackanko-arcarchako-rackan-rackanko-arcarchanko-rarkeanko-arcarchanko-rack。
A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations. The inverse scattering problem on the whole axis are examined in the case where linear system becomes the classical Zakharov--Shabat system consists of two equations and admits a real symmetric and real anti-symmetric potential. Referring to these results, the N--soliton solutions for the integro-differential version of the nonlinear Klein--Gordon equation coupled with a scalar field (CKG) and negative order modified Korteweg-de Vries (nmKdV) equation are obtained by using the inverse scattering method via the Gel'fand--Levitan--Marchenko equation.
