Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations
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In this paper, we study solitary wave solutions of the Cauchy problem for Half-wave-Schrödinger equation in the plane. First, we show the existence and the orbital stability of the ground states. Second, we prove that given any speed [Formula: see text], traveling wave solutions exist and converge to the zero wave as the velocity tends to [Formula: see text]. Finally, we solve the Cauchy problem for initial data in [Formula: see text], with [Formula: see text]. The critical case [Formula: see text] still stands as an interesting open problem.
2017 ◽
Vol 146
(4)
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pp. 1537-1550
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2002 ◽
Vol 185
(2)
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pp. 437-482
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2017 ◽
Vol 37
(4)
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pp. 998-1018
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2012 ◽
Vol 22
(12)
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pp. 1250305
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2019 ◽
Vol 9
(6)
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pp. 2389-2408
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2014 ◽
Vol 6
(2)
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pp. 273-284
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