Bilinearization and soliton solutions of N=1 supersymmetric coupled dispersionless integrable system

Abstract

An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable variable transformation, the SUSY-CD integrable system is equivalent to N=1 supersymmetric sine-Gordon equation. A superfield bilinear form of SUSY-CD integrable system has been proposed by using super Hirota operator. Explicit expressions of superfield soliton solutions of SUSY-CD integrable system have been obtained by using the Hirota method.

Stable soliton solutions to the nonlinear low-pass electrical transmission lines and the Cahn-Allen equation

“…The exact solutions can also serve as the basis for the excellence and precision of computer algebra software in solving NLEEs. Therefore, a number of important methods for the explicit and detailed stable soliton solutions of nonlinear physical models have currently been developed with the aid of Matlab, Mathematica, etc., such as, the differential transformation [1] method, the Hirota's bilinear method [2] , [3] , [4] , [5] , the approach of modified simple equation [6] , [7] , the F-expansion method [8] , the Exp-function [9] method, the modified exponential-function method [10] , the -expansion [11] , [12] , [13] scheme, the improved -expansion method [14] , the rational -method [15] , the extended trial equation method [16] , the improved -expansion method [17] , the first integral method [18] , the generalized Kudryashov [19] approach, the homotopy analysis [20] technique, the mean finite difference Monte-Carlo [21] method, the sine-Gordon expansion method [22] , the -expansion method [23] , the modified Kudryashov [24] scheme, the Adomian decomposition method [25] , the generalized projective Riccati equation method [26] , the multi-symplectic Runge-Kutta method [27] , the -expansion method [28] , the modified extended tanh method [29] , [30] , the exponential rational function method [31] , the generalized rational function method [32] , the unified method [33] , [34] ,…”

“…The exact solutions can also serve as the basis for the excellence and precision of computer algebra software in solving NLEEs. Therefore, a number of important methods for the explicit and detailed stable soliton solutions of nonlinear physical models have currently been developed with the aid of Matlab, Mathematica, etc., such as, the differential transformation [1] method, the Hirota's bilinear method [2,3,4,5], the approach of modified simple equation [6,7], the F-expansion method [8], the Exp-function [9] method, the modified exponential-function method [10], the ( ′ ∕ )-expansion [11,12,13] scheme, the improved ( ′ ∕ )-expansion method [14], the rational ( ′ ∕ )-method [15], the extended trial equation method [16], the improved tan ( ( )∕2)-expansion method [17], the first integral * Corresponding author. E-mail address: ali_math74@yahoo.com (M.A.…”

Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method

“…Recently, a number of powerful techniques have been developed to extract exact and explicit solutions of nonlinear physical models with the help of computer algebra, like Maple, Matlab and Mathematica. These include, the differential transform method (Yang, Tenreiro Machado, & Srivastava, 2016), the modified simple equation method and its various extensions (Arnous et al, 2017), the Hirto's bilinear method (Mirza & Hassan, 2017), the sinecosine method (Mirzazadeh et al, 2015), the tanhfunction expansion and its various modifications (Zdravkovi c, Kavitha, Satari c, Zekovi c, & Petrovi c, 2012), the F-expansion method (Akbar & Ali, 2017), the Exp-function method (Zhang, Li, & Zhang, 2016), the modified simple equation method (Khan & Akbar, 2013), the modified exponential function method (Abdelrahman, Zahran, & Khater, 2015), the ðG 0 =GÞ-expansion method (Akbar, Ali, & Roy, 2018;Chen & Li, 2012;Manafian, Lakestani, & Bekir, 2016), the rational ðG 0 =GÞ-expansion method (Islam, Akbar, & Azad, 2018), the extended trial equation method , the improved tan /ðnÞ ð Þ-expansion method (Mohyud-Din, , the first integral method (Ekici et al, 2016), the homogeneous balance method (Senthilvelan, 2001), the homotopy analysis method (Noor, Haq, Abbasbandy, & Hashim, 2016), the mean Monte Carlo finite difference method (Mohammed, Ibrahim, Siri, & Noor, 2019), the fractional Riccati method and fractional double function method (Wang, Lu, Dai, & Chen, 2020;Wu, Yu, & Wang, 2020), the projective Riccati equation method (Dai, Fan, & Zhang, 2019), the Taylor series method (He, Shen, Ji, & He, 2020;, the variational iteration method (He, 2000(He, , 2011He & Jin, 2020;He & Latifizadeh, 2020), the modified variational iteration algorithms (Ahmad, Khan, & Cesarano, 2019;Ahmad, Khan, & Yao, 2020;…”

Bilinearization and soliton solutions of the supersymmetric coupled KdV equation

“…Свои SUSY-версии имеют многие известные классические интегрируемые системы, например связанная бездисперсионная интегрируемая система, уравнение синус-Гордон, уравнение Кортевега-де Фриза (KдФ), иерархия Кадомцева-Петвиашвили, нелинейное уравнение Шредингера, уравнение Буссинеска и т. д. [6]- [14].…”