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Painlevé analysis and new class of novel solutions for (2+1)-dimensional 3-component coupled nonlinear Maccari’s system
In this work, Painlevé analysis is used to examine the integrability of the (2+1)-dimensional 3-component coupled nonlinear Maccari’s system....
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Painlevé integrability and superposition wave solutions of Whitham–Broer–Kaup equations
In this paper, the Painlevé integrability and superposition wave solutions of Whitham–Broer–Kaup (WBK) equations are studied, which can help us...
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Painlevé integrability and lump solutions for two extended (3 + 1)- and (2 + 1)-dimensional Kadomtsev–Petviashvili equations
The current work introduces two extended (3 + 1)- and (2 + 1)-dimensional Painlevé integrable Kadomtsev–Petviashvili (KP) equations. The...
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Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system
In this article, Painlevé analysis is employed to test the integrability of (2+1)-dimensional long wave–short wave resonance interaction system using...
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A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas
This paper proposes a new integrable generalized (3+1)-dimensional nonlinear partial differential equation. We apply the standard Painlevé test to...
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Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2\(+\)1)-dimensional generalized Burgers system with the variable coefficients in a fluid
Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a...
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Two new Painlevé integrable KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation
In this work, we develop two new (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS...
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Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves
In soliton theory and nonlinear waves, this research proposes a new Painlevé integrable generalized (3+1)-D evolution equation. It demonstrates the...
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Non-collisional dynamics of (2+1)-dimensional Broer-Kaup-Kupershmidt system
In this communication, the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is studied. With the aid of Painlevé Bäcklund transformation method,...
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Nonlocal residual symmetries, N-th Bäcklund transformations and exact interaction solutions for a generalized Broer–Kaup–Kupershmidt system
The nonlocal residual symmetries of a generalized Broer–Kaup–Kupershmidt system are constructed using the truncated Painlevé expansion. By...
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On mKdV and associated classes of moving boundary problems: reciprocal connections
A class of Stefan-type moving boundary problems for the canonical modified Korteweg–de Vries (mKdV) equation of soliton theory is solved via...
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Integrability, bilinearization, Bäcklund transformations and solutions for a generalized variable-coefficient Gardner equation with an external-force term in a fluid or plasma
A generalized variable-coefficient Gardner equation with an external-force term is investigated which can model the propagation and interaction of...
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Characteristic of integrability of nonautonomous KP-modified KP equation and its qualitative studies: soliton, shock, periodic waves, breather, positons and soliton interactions
This article demonstrates the characteristic of integrability of the nonautonomous KP-mKP equation through Painlevé analysis, bilinear Bäcklund and...
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Bilinearization and new center-controlled N-rogue solutions to a (3+1)-dimensional generalized KdV-type equation in plasmas via direct symbolic approach
This research studies rogue wave solutions with center parameters of a generalized (3+1)-dimensional KdV-type equation in plasma physics. Using a...
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Integrable (3+1)-dimensional Ito equation: variety of lump solutions and multiple-soliton solutions
In this work, we study an extended integrable (3+1)-dimensional Ito equation, where its complete integrability is justified via Painlevé analysis....
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Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed
This paper focuses on the exact soliton solutions of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equations with time-dependent linear phase...
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A variety of new rogue wave patterns for three coupled nonlinear Maccari’s models in complex form
Maccari’s system serves as a valuable tool in various mathematical disciplines, contributing to the understanding of complex dynamics, control...
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A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions
Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This...
