On the resonant interaction of spherical ion-acoustic solitons

Lonngren, Karl E.; Gabl, E. F.; Bulson, Jeffry M.; Khazei, Mahyar

doi:10.1016/0167-2789(83)90278-6

Physica D: Nonlinear Phenomena

1983

DOI: 10.1016/0167-2789(83)90278-6

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On the resonant interaction of spherical ion-acoustic solitons

Karl E. Lonngren

E. F. Gabl

Jeffry M. Bulson

et al.

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1984

2007

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Cited by 7 publications

(1 citation statement)

References 21 publications

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“…Moreover, since aspects of Miles' resonance have been experimentally verified [19,20], we expect that it will also be possible to observe the more general interactions described here.…”

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confidence: 65%

Line Soliton Interactions of the Kadomtsev-Petviashvili Equation

Biondini

2007

Phys. Rev. Lett.

134

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We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line solitons as y-->-infinity. We also show that the (2N-1)!! types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.

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“…Moreover, since aspects of Miles' resonance have been experimentally verified [19,20], we expect that it will also be possible to observe the more general interactions described here.…”

mentioning

confidence: 65%

Line Soliton Interactions of the Kadomtsev-Petviashvili Equation

Biondini

2007

Phys. Rev. Lett.

134

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Soliton solutions of the Kadomtsev-Petviashvili II equation

Biondini

Chakravarty

2006

Journal of Mathematical Physics

116

654

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We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the taufunction, we explicitly characterize the incoming and outgoing line-solitons of this class of solutions. We illustrate these results by discussing several examples.

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Axially symmetric propagation of small-amplitude ion-acoustic waves

Herman

1990

Physics of Fluids B: Plasma Physics

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On the resonant interaction of spherical ion-acoustic solitons

Cited by 7 publications

References 21 publications

Line Soliton Interactions of the Kadomtsev-Petviashvili Equation

Line Soliton Interactions of the Kadomtsev-Petviashvili Equation

Soliton solutions of the Kadomtsev-Petviashvili II equation

Axially symmetric propagation of small-amplitude ion-acoustic waves

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