THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION

Acta mathematica scientia,Series B ›› 1995, Vol. 15 ›› Issue (2): 196-206.

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THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION

Feng Xueshang

Numerical Laboratory for Heliospheric physics, P. O. BOX 8701, Beijing 10008 G. China

Received:1993-02-26 Revised:1994-05-28 Online:1995-06-25 Published:1995-06-25
Supported by:
Supported by the NSF of China.

Abstract

Abstract: Is this Paper, the global existence of smooth solutions to the initial value problem for the fourth order nonlinear Schrödinger equation in the Lax hierarchy of the nonlinear Schrödinger equation(NLS equation) is established by using the so-called continuation method and delicate a priori estimate. In addition, the asymptotic properties of the solutions as |x|→+∞ are discussed.

Key words: Forth order nonlinear schrodinger equation, Initial value problem, Global existence, Asymptotic behavior

Feng Xueshang. THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION[J].Acta mathematica scientia,Series B, 1995, 15(2): 196-206.

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THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION

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