On the 2D Zakharov system withL2Schrödinger data
نویسندگان
چکیده
منابع مشابه
Regularity Bounds on Zakharov System Evolutions
Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution u(t) is shown to satisfy an estimate ‖u(t)‖ Hs ≤ C|t|, where H is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrödinger equation which reduces matters to bilinear estimates.
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We prove that the initial value problem for the two-dimensional modified ZakharovKuznetsov equation is locally well-posed for data in H(R), s > 3/4. Even though the critical space for this equation is L(R) we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.
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The dressing procedure for the Generalised Zakharov-Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax...
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2003 Acknowledgments I would like to thank my supervisor, Dr. Bao Weizhu, who gave me the opportunity to work on such an interesting research project, paid patient guidance to me, reviewed my thesis and gave me much invaluable help and constructive suggestion on it. It is also my pleasure to express my appreciation and gratitude to A/P Wei Guowei, from whom I got effective training on programmi...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2009
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/22/5/007