
 
Quasiperiodic Solutions for the Derivative Nonlinear SchrÖdinger Equation with Finitely Differentiable Nonlinearities 
 
Citation： 
Meina GAO,Kangkang ZHANG.Quasiperiodic Solutions for the Derivative Nonlinear SchrÖdinger Equation with Finitely Differentiable Nonlinearities[J].Chinese Annals of Mathematics B,2017,38(3):759~786 
Page view： 1414
Net amount： 982 
Authors： 
Meina GAO; Kangkang ZHANG 
Foundation： 
This work was supported by the National Natural Science
Foundation of China (No.11201292), Shanghai Natural Science
Foundation (No.12ZR1444300) and the Key Discipline "Applied
Mathematics" of Shanghai Second Polytechnic University
(No.XXKZD1304). 


Abstract： 
The authors are concerned with a class of derivative nonlinear
Schr\"{o}dinger equation
$$\mathbf{i} u_t+u_{xx}+\mathbf{i} \epsilon f(u,\ov{u}, \omega t)u_x=0, \quad (t,x)\in\mathbb{R}\times [0, \pi],$$
subject to Dirichlet boundary condition, where the nonlinearity $f(z_1,z_2,\phi)$ is merely finitely
differentiable with respect to all variables rather than analytic
and quasiperiodically forced in time. By developing a smoothing and
approximation theory, the existence of many quasiperiodic
solutions of the above equation is proved. 
Keywords： 
Derivative NLS, KAM theory, Newton iterative scheme, Reduction
theory, Quasiperiodic solutions, Smoothing techniques 
Classification： 
37K55, 35B15, 35J10,
35Q40, 35Q55 

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