Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5792
Abstract: We consider the fully parity‐time (PT) symmetric nonlocal (2 + 1)‐dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N‐soliton solutions of the nonlocal NLS… read more here.
Keywords: semi rational; rational solutions; nonlocal dimensional; nonlinear schr ... See more keywords
Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation
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DOI: 10.1007/s11071-017-4033-9
Abstract: A new variant of the $$(2+1)$$(2+1)-dimensional [$$(2+1)d$$(2+1)d] Boussinesq equation was recently introduced by Zhu [Line soliton and rational solutions to (2+1)-dimensional Boussinesq equation by Dbar problem, 2017. arXiv:1704.02779v2; see eq. (3)]. First, we derive in this… read more here.
Keywords: rational solutions; dimensional boussinesq; soliton; boussinesq equation ... See more keywords
Rational solutions of the classical Boussinesq–Burgers system
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DOI: 10.1007/s11071-018-4424-6
Abstract: We study rational solutions of the classical Boussinesq–Burgers (CBB) system which describes the propagation of shallow water waves. The main tools applied in this work to derive these solutions are the bilinear method and the… read more here.
Keywords: system; solutions classical; rational solutions; boussinesq burgers ... See more keywords
The mKdV equation and multi-parameters rational solutions
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DOI: 10.1016/j.wavemoti.2020.102667
Abstract: Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters… read more here.
Keywords: multi parameters; parameters rational; rational solutions; mkdv equation ... See more keywords
Rational solutions to the KPI equation from particular polynomials
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DOI: 10.1016/j.wavemoti.2021.102828
Abstract: Abstract We construct solutions to the Kadomtsev–Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second spatial derivative of a logarithm of a determinant of order n . We obtain with… read more here.
Keywords: equation particular; rational solutions; equation; particular polynomials ... See more keywords
AKNS and NLS hierarchies, MRW solutions, Pn breathers, and beyond
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DOI: 10.1063/1.5049949
Abstract: We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its… read more here.
Keywords: quasi rational; rational solutions; deformed versions; akns hierarchy ... See more keywords
Resonant collisions of high-order localized waves in the Maccari system
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DOI: 10.1063/5.0141546
Abstract: Exploring new nonlinear wave solutions to integrable systems has always been an open issue in physics, applied mathematics, and engineering. In this paper, the Maccari system, a two-dimensional analog of nonlinear Schr[Formula: see text]dinger equation,… read more here.
Keywords: system; resonant collisions; physics; maccari system ... See more keywords
Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1080/14029251.2019.1544793
Abstract: We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV)… read more here.
Keywords: adler bobenko; rational solutions; nqc equation; bobenko suris ... See more keywords
Rational solutions to two Sawada–Kotera-like equations
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DOI: 10.1142/s0217984919501082
Abstract: Two Sawada–Kotera-like equations are introduced by the generalized bilinear operators [Formula: see text] associated with two prime numbers [Formula: see text] and [Formula: see text], respectively. Rational solutions of the two presented Sawada–Kotera-like equations are… read more here.
Keywords: kotera like; rational solutions; like equations; two sawada ... See more keywords
Breathers, rogue waves and semi-rational solutions for a Heisenberg ferromagnet-type equation
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DOI: 10.1142/s0217984923500537
Abstract: The Kuralay equation, as a Heisenberg ferromagnet-type equation, is of great significance for describing nonlinear phenomena in magnets. For the Kuralay-IIA equation, based on the constructed [Formula: see text]-fold Darboux transformation, we derive its one-fold… read more here.
Keywords: equation; heisenberg ferromagnet; ferromagnet type; rational solutions ... See more keywords
Rational and Semi-Rational Solutions to the (2 + 1)-Dimensional Maccari System
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DOI: 10.3390/axioms11090472
Abstract: The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique,… read more here.
Keywords: maccari system; rational solutions; rational semi; semi rational ... See more keywords