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
Investigation of the new optical soliton solutions to the (2+1)-dimensional calogero-bogoyavlenskii schiff model
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DOI: 10.1038/s41598-024-83552-8
Abstract: In this work, we use the ansatz transformation functions to investigate different analytical rational solutions by symbolic computation. For the (2+1)-dimensional Calogero-Bogoyavlenskii Schiff (CBS) model, we derive a variety of rational solutions, such as homoclinic… read more here.
Keywords: rational solutions; calogero bogoyavlenskii; model; bogoyavlenskii schiff ... See more keywords
AKNS and NLS hierarchies, MRW solutions, Pn breathers, and beyond
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Physics"
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
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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
Polynomial Analogs of Theta Functions and Rational Solutions of the KP Equation
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DOI: 10.1093/imrn/rnae227
Abstract: In this paper we classify the singular curves whose theta divisors in their generalized Jacobians are algebraic, meaning that they are cut out by polynomial analogs of theta functions. We also determine the degree of… read more here.
Keywords: rational solutions; theta functions; solutions equation; functions rational ... 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