Results 1 to 10 of about 3,184 (198)

A search method for Hirota bilinear systems of nonlinear evolution equations

Next Research
We present a systematic search method for finding Hirota bilinear systems of nonlinear evolution equations, with emphasis on the nonlinear Schrödinger equation (NLSE). Using a known exact solution, couplings between the different terms of the differential equation are identified, which are then used to derive the bilinear system.
I. Albazlamit, L. Al Sakkaf, U. Al Khawaja   +2 more
openaire   +2 more sources

New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

Abstract and Applied Analysis, 2014
Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation.
Gui-qiong Xu
doaj   +1 more source

Constructing various wave symmetries on the blood flow and arterial wall motion model using the Hirota bilinear method

Results in Engineering
In this research, the Hirota bilinear method is used for the development and examination of different types of wave symmetries of a blood flow and arterial wall motion model.
Baboucarr Ceesay, Nauman Ahmed, Muhammad Zafarullah Baber, Zafar Iqbal, Ali Akgül   +4 more
doaj   +1 more source

Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

, 1997
Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered.
B. G. Konopelchenko, L. V. Bogdanov, Nizhnik L. P., Sato M., Ueno K., Veselov A. P., Zakharov V. E., Zakharov V. E.   +7 more
core   +1 more source

Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

, 2007
We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe
A. Baha Balantekin, A. Klümper, A. Kuniba, A. V. Zabrodin, A. V. Zabrodin, A. V. Zabrodin, A. Zabrodin, E. Date, I. Bars, I. Krichever, I. Macdonald, L. A. Takhtadzhan, L. Faddeev, N. M. Bogoliubov, N. Shinzawa, N. Shinzawa, P. Kulish, P. P. Kulish, P. P. Kulish, R. Hirota, S. Saito, V. Bazhanov, V. Kac, Z. Tsuboi   +23 more
core   +2 more sources

The bilinear neural network method for solving Benney–Luke equation

Partial Differential Equations in Applied Mathematics
Benney–Luke equation, the estimation of water wave propagation on the water’s surface, is significantly important in studying the tension of water waves in physics.
Nguyen Minh Tuan, Sanoe Koonprasert, Sekson Sirisubtawee, Phayung Meesad   +3 more
doaj   +1 more source

A class of lump solutions and localized excitations for the generalized (3 + 1)-dimensional KP equation

Results in Physics, 2020
Based on symbolic computation and Hirota bilinear form, a class of lump solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation is given. As a result, the lump solution shows a new perspective to knowledge them. Meanwhile,
Ping Cui
doaj   +1 more source

The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation

, 2001
In this paper, some notes of the homogeneous balance (HB) method are discussed by a kind of general fifth-order KdV (fKdV) equation. Frist, the auto-B\"acklund transformation and lax represents of the higher-order KdV equation(a specific forms of fKdV ...
Fajiang, Zhang, Lei, Yang, Yinghai, Wang
core   +2 more sources

New solution of the $\mathcal{N}=2$ Supersymmetric KdV equation via Hirota methods

, 2012
We consider the resolution of the $\mathcal{N}=2$ supersymmetric KdV equation with $a=-2$ ($SKdV_{a=-2}$) from the Hirota formalism. For the first time, a bilinear form of the $SKdV_{a=-2}$ equation is constructed. We construct multisoliton solutions and
Carstea A S, Carstea A S, Drazin P G, Francois Gieres, Fukutani S, Ghosh S, Hussin V, Laurent Delisle, Véronique Hussin   +8 more
core   +1 more source

Unification of integrable q-difference equations

Electronic Journal of Differential Equations, 2015
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions ...
Burcu Silindir, Duygu Soyoglu
doaj