Results 61 to 70 of about 3,238 (183)

Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism

, 1994
We introduce multilinear operators, that generalize Hirota's bilinear $D$ operator, based on the principle of gauge invariance of the $\tau$ functions.
A. Ramani, B. Grammaticos, Grammaticos, Hietarinta, Hietarinta, Hietarinta, Hietarinta, Hirota, Hirota, J. Hietarinta, Kaup, Kupershmidt, Matsukidaira, Morris, Sawada, Schiff   +15 more
core   +1 more source

The Dynamical Landscape of the Negative‐Order (3+1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Equation

Journal of Mathematics, Volume 2026, Issue 1, 2026.
A new negative‐order form of the (3 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical engineering applications.
Ulviye Demirbilek, Jan Muhammad, Arzu Akbulut, Usman Younas, Taha Radwan, Karim K. Ahmed, Dimitri Mugnai   +6 more
wiley   +1 more source

Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods [PDF]

, 2017
This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.
Wiggins, Benjamin
core   +1 more source

Dynamical Analysis of Wave Solutions for the Complex Ginzburg−Landau and (4 + 1)‐Dimensional Fokas Equations With Beta Derivative

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study propounds a detailed report on the exact wave solutions of the complex fractional Ginzburg−Landau equation (CFGLE) with quadratic‐cubic law nonlinearity and (4 + 1)‐dimensional fractional Fokas equation (FFE). For this purpose, the aforementioned equations are transformed into nonlinear ordinary differential equations (NLODEs) within the ...
Özlem Kırcı, Yusuf Pandır, Yusuf Gurefe, Hussain Juya, Yongqiang Fu   +4 more
wiley   +1 more source

Exploring soliton dynamics and wave interactions in an extended Kadomtsev-Petviashvili-Boussinesq equation

Ain Shams Engineering Journal
This research investigates the extended Kadomtsev-Petviashvili-Boussinesq equation, relevant in numerous scenarios involving dissipative media. To initiate the analysis, a Hirota bilinear form is applied, leading to a Bäcklund transformation for the ...
Nauman Raza, Adil Jhangeer, Zeeshan Amjad, Beenish Rani, Dumitru Baleanu   +4 more
doaj   +1 more source

Constructing a Supersymmetric Integrable System from the Hirota Method in Superspace

, 2004
An N=1 supersymmetric system is constructed and its integrability is shown by obtaining three soliton solutions for it using the supersymmetric version of Hirota's direct method.Comment: 10 pages, no ...
Carstea, Carstea, Carstea, Das, Debojit Sarma, Gardner, Ghosh, Ghosh, Hieteranta, Hieteranta, Hirota, Hirota, Hirota, Hirota, Hirota, Kakei, Kortweg, Kupershmidt, Labelle, Laberge, Manin, Mathieu, Mathieu, McArthur, Popowicz, Satsuma   +25 more
core   +1 more source

Woody cover and geology as regional‐scale determinants of semi‐arid savanna stability

Remote Sensing in Ecology and Conservation, Volume 11, Issue 5, Page 539-554, October 2025.
Savannas are vital for global biodiversity and carbon storage, yet their responses to climate change and human activity remain uncertain. Using remote sensing time series and Bayesian Linear Models, we show that drought resistance and resilience vary regionally, shaped by complex interactions between geology, woody cover, fire regimes, past climate ...
Liezl Mari Vermeulen, Koenraad Van Meerbeek, Paulo Negri Bernardino, Jasper Slingsby, Bruno Verbist, Ben Somers   +5 more
wiley   +1 more source

Multi-soliton solutions of the Sawada-Kotera equation using the Hirota direct method: Novel insights into nonlinear evolution equations

Partial Differential Equations in Applied Mathematics, 2023
Recently, mathematicians, engineers, and scientists have explored the unique characteristics and potential applications of multi-solitons, which is an expanding domain of study.
A. K. M. Kazi Sazzad Hossain, M. Ali Akbar   +1 more
doaj   +1 more source

Novel Nonlinear Dynamical Solutions to the (2 + 1)‐Dimensional Variable Coefficients Equation Arise in Oceanography

Engineering Reports, Volume 7, Issue 6, June 2025.
This study explores novel nonlinear dynamical solutions to the (2 + 1)‐dimensional variable coefficient equation in oceanography. Using the Hirota bilinear method, we derive multi‐soliton, M‐lump, and hybrid wave solutions, revealing collision phenomena and their physical significance in nonlinear fluid dynamics and mathematical physics.
Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, Shams Forruque Ahmed   +3 more
wiley   +1 more source

Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation

Journal of Applied Mathematics, 2019
Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by ...
Yanni Zhang, Jing Pang
doaj   +1 more source