Evolution of three-dimensional nonlinear pulses in weakly dispersive media

Karpman, V. I.; Belashov, V. Yu.

doi:10.1016/0375-9601(91)90751-s

Cited by 35 publications

(19 citation statements)

References 1 publication

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“…Class (1.18) has been studied recently in [36,39] (see also [19,20,24,26,34,35,40,45] for studies of subclasses of (1.18), and in particular for the original KadomtserPetviashvili equation). In this script, attention will be given to the collection of models depicted in (1.19).…”

Section: Cauchy Problem and Solitary-wave Solutionsmentioning

confidence: 99%

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The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

Bona¹,

Liu²,

Tom³

2002

Journal of Differential Equations

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Section: Cauchy Problem and Solitary-wave Solutionsmentioning

confidence: 99%

“…It follows from this relation that In these inequalities, use has been made of the fact that juj 1 is bounded on ½0; T by virtue of the condition u where a is a monotone increasing function (see [26] …”

mentioning

confidence: 98%

The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

Bona¹,

Liu²,

Tom³

2002

Journal of Differential Equations

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“…Remark 5.1. -Solitary waves for (5.1) (5.2) have been observed numerically for 03B4 = -1, p = 1 in [3], [ 11 ], [12].…”

Section: An Extension and Final Remarksmentioning

confidence: 99%

Solitary waves of generalized Kadomtsev–Petviashvili equations

Bouard

Saut

1997

Ann. Inst. H. Poincaré C Anal. Non Linéaire

159

221

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L'accès aux archives de la revue « Annales de l'I. H. P., section C » (http://www.elsevier.com/locate/anihpc) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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“…(16) below). In the case of KP-I type equations (;>0 or ;=0, :<0) we can not gain the x derivative using the relation (16). However, using the parabolic regularisation method it is possible to prove local well-posedness of (1) in H s , s>2 and local wellposedness of (2) in H s , s>5Â2 (cf.…”

Section: Introductionmentioning

confidence: 97%

“…Such equations occur naturally in the modeling of certain long dispersive waves (cf. [2,15,16]). The study of their solitary wave solutions was done in [6,7].…”

Section: Introductionmentioning

confidence: 97%

The Cauchy Problem for Higher-Order KP Equations

Saut

Tzvetkov

1999

Journal of Differential Equations

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We study the local well-posedness of higher-order KP equations. Our well-posedness results make an essential use of a global smoothing effect for the linearized equation established in Ben-Artzi and Saut (preprint, 1997), injected into the framework of Fourier transform restriction spaces introduced by Bourgain. Our illposedness results rely on the existence of solitary wave solutions and on scaling arguments. The method was first applied in the context of the KdV and Schro dinger equations (cf.

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Evolution of three-dimensional nonlinear pulses in weakly dispersive media

Cited by 35 publications

References 1 publication

The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

Solitary waves of generalized Kadomtsev–Petviashvili equations

The Cauchy Problem for Higher-Order KP Equations

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