Soliton propagation in three coupled nonlinear Schrödinger equations

Abrarov, R. M.; Christiansen, Peter Leth; Darmanyan, S.; Scott, Alwyn C.; Soerensen, M. P.

doi:10.1016/0375-9601(92)90647-5

Cited by 15 publications

(13 citation statements)

References 11 publications

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“…the spectral problem (3) and ( 4) can transform to Ψ [1] x = (iσλ 2 + Q [1] λ)Ψ [1] = U [1] Ψ [1] , Ψ…”

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

“…(3) invariant under the gauge transformation Eq. (5), it is crucial to find a matrix T so that U [1] , V [1] have the same forms as U , V . At the same time, the old solution (q, q(−x, −t)) in spectral matrixes U , V are mapped into new solution (q [1], q [1](−x, −t)) in transformed spectral matrixes U [1] , V [1] .…”

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

“…So a 0 , b 0 , c 0 , d 0 are constants, a 1 , d 1 are undetermined functions about x and t. And the new solution q [1] can be shown in the following DT formula which is obtained by the Eq. ( 11)…”

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

“…Nonlinear evolution equations play an important role and their solutions have been a hot research spot, including soliton [1,2,3,4], breather [5,6,7], rogue wave [8,9,10,11] and others [12,13,14,15]. The derivative nonlinear Schrödinger equation (DNLS) [16,17,18,19] iq t − q xx + i(q 2 q * ) x = 0, (…”

Section: Introductionmentioning

confidence: 99%

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Breathers and Rogue Waves On The Double-Periodic Background for The Reverse-Space-Time Derivative Nonlinear Schrödinger Equation

Zhou

Chen

2021

Preprint

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The dynamic behaviors of the solutions for the reverse-space-time derivative nonlinear Schrödinger equation are studied by Darboux transformation. The breathers on the periodic and double-periodic background are derived by the N -fold Darboux transformation. The rogue waves on the periodic and double-periodic background are constructed by the generalized Darboux transformation. It is worth mentioning that the breathers and rogue waves on double-periodic background based on the plane wave seed solution are first constructed. The two peak, four peak rogue waves on the double-periodic background are found. And the rogue waves on the double-periodic background can be transformed into the classical rogue wave on the plane wave background with a special reduction relation.

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“…the spectral problem (3) and ( 4) can transform to Ψ [1] x = (iσλ 2 + Q [1] λ)Ψ [1] = U [1] Ψ [1] , Ψ…”

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

Section: One-fold Dt Of the Reverse-space-time Dnls Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Breathers and Rogue Waves On The Double-Periodic Background for The Reverse-Space-Time Derivative Nonlinear Schrödinger Equation

Zhou

Chen

2021

Preprint

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“…The term soliton had been coined earlier by Zabusky and Kruskal for a pulse-like nonlinear wave (now called a solitary wave), emerging with unchanged shape and speed, for example, from multi-pulse collisions [15]. Since then, multitudes of soliton wave equations have been found in applied sciences [16][17][18][19]. Among other things, during one visit to Heriot-Watt University in Scotland, UK, in 1995, Alwyn contributed to a successful experimental recreation of the Scott Russell's soliton [20].…”

mentioning

confidence: 99%

Editorial Note

Curtu

Jørgensen

2011

Acta Appl Math

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Saddened by the news of Alwyn Scott's death, the editors of Acta Applicandae Mathematicae (ACAP) decided to dedicate to his memory, a special issue of the journal. At the end of 2008 invitation letters were sent to former Al Scott's collaborators and to the international scientific community. They laid out the plan of a volume with focus on several topics Al was involved in: nonlinear diffusion, Josephson (superconducting) transmission lines, coupled anharmonic oscillators, neural systems and biomolecular dynamics. Another publication project was then underway ([1]; solitons in biology) but ACAP editors felt that it had a more limited scope. The special issue planned by ACAP aimed to reach out to a variety of fields and communicate across disciplines; it did not wish to place limitations on what prospective authors might have felt important, and it encouraged submission of both research articles and review articles as a mix. While positive feedback was received from colleagues, the project has been delayed for couple of years due to unforseen events. It is a pleasure to announce now its completion and to see it in final publication form.Alwyn Scott was an editor for Acta Applicandae Mathematicae from the beginning. The founding editor of ACAP was Michiel Hazewinkel and the first journal issue appeared in 1983. Alwyn Scott and one of the present editors (Palle Jorgensen), were part of this event. Jorgensen recalls how Alwyn, and the other members of the initial editorial board, shared Michiel's vision for the journal. At the time, over the phone and in wider mathematical circles, Michiel vigorously articulated and promoted his ideas and willingness to take risks in nurturing a forward looking and truly interdisciplinary journal. The nineteen-eighties were a period witnessing solutions of deep problems in mathematics. At the same time, an increased distance between mathematics and its applications could be sensed. Back then, and perhaps even today, one sees trends in mathematics with increasing specialization (overspecialization); a tendency for researchers to narrow their focus, specialist authors to write

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Optical Solitons in Fibers

Maĭmistov

Башаров

1999

Nonlinear Optical Waves

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Soliton propagation in three coupled nonlinear Schrödinger equations

Cited by 15 publications

References 11 publications

Breathers and Rogue Waves On The Double-Periodic Background for The Reverse-Space-Time Derivative Nonlinear Schrödinger Equation

Breathers and Rogue Waves On The Double-Periodic Background for The Reverse-Space-Time Derivative Nonlinear Schrödinger Equation

Editorial Note

Optical Solitons in Fibers

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