We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove tha...We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs.展开更多
The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the sc...The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the scattering operator, which improves the known results in some sense.展开更多
Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda &...Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.展开更多
We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger eq...We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where s≥n/2 is arbitrary and n≥2. Therefore, the scattering operators are infinitely smooth for the above two equations.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 19901007 and 19871020).
文摘We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs.
基金Supported by Natural Science Foundation of China(Grant No.10931007)Zhejiang Provincial NaturalScience Foundation of China(Grant No.Y6090158)
文摘The scattering problem for the Klein–Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein–Gordon equation, we prove the existence of the scattering operator, which improves the known results in some sense.
文摘Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.
基金Supported by the National Natural Science Foundation of China. Grant 19901007.
文摘We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where s≥n/2 is arbitrary and n≥2. Therefore, the scattering operators are infinitely smooth for the above two equations.
