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Blow-up Solutions for Mixed Nonlinear Schrödinger Equations

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Abstract

This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation:

$$ \phi _{t} = i\alpha \phi _{{xx}} + \beta \phi ^{2} {\mathop \phi \limits^ - }_{x} + \gamma {\left| \phi \right|}^{2} \phi _{x} + ig{\left( {{\left| \phi \right|}^{2} } \right)}\phi . $$

Under certain conditions on the initial data and the function g(s), we study the existence and nonexistence of global solution for this equation. The blow-up solution and the blow-up time are also investigated.

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Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen, 361005, P. R. China

    Shao Bin Tan

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  1. Shao Bin Tan
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Correspondence to Shao Bin Tan.

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Supported by the National Science Foundation of China (No. 10071061)

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Tan, S.B. Blow-up Solutions for Mixed Nonlinear Schrödinger Equations. Acta Math Sinica 20, 115–124 (2004). https://doi.org/10.1007/s10114-003-0295-x

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  • DOI: https://doi.org/10.1007/s10114-003-0295-x

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