Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

Sadat, R.; Kassem, M.

doi:10.3390/mca23010015

Cited by 12 publications

(21 citation statements)

References 16 publications

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“…Substituting from (24) and (23) in to (16) and setting the coefficients of ϕ(η) to be zero, we obtain an algebraic system in a 0 ,a 1 ,b 1 , and d i ( i = 0, …, 2). Solving this system, we obtain a set of solutions: Case 1:…”

Section: Riccati Equation Methodsmentioning

confidence: 99%

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Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Saleh

Sadat

Kassem

2019

Math Methods in App Sciences

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We explored and specialized new Lie infinitesimals for the (3 + 1)-dimensional B-Kadomtsev-Petviashvii (BKP) using the commutation product, which results a system of nonlinear ODEs manually solved. Through two stages of Lie symmetry reduction, (3 + 1)-dimensional BKP equation is reduced to nonsolvable nonlinear ODEs using various combinations of optimal Lie vectors.Using the integration and Riccati equation methods, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solutions for BKP. Some selected solutions illustrated through three-dimensional plots. KEYWORDS(3 + 1)-dimensional B-Kadomtsev-Petviashvii (BKP), integrating factor, partial differential equations, Riccati equation, symmetry analysis MSC CLASSIFICATION

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Section: Riccati Equation Methodsmentioning

confidence: 99%

“…Here, based on Lie algebra, 22 we optimize Lie vectors containing arbitrary functions of time through a commutative product. Through two stages of reductions, some ODEs that had no quadrature are solved using an the integrating factor 23 and Riccati equation method.…”

Section: Introductionmentioning

confidence: 99%

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Saleh

Sadat

Kassem

2019

Math Methods in App Sciences

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“…The series in (17) contains an infinite number of terms for a smooth function ( ). Therefore, we have ⟨HOBW ( ) , HOBW ( )⟩ = ⟨ ( ) , HOBW ( )⟩ (21) so that…”

Section: Function Approximation By Using the Hobw Functionsmentioning

confidence: 99%

“…where the matrix P 2 −1 ×2 −1 is called the HOBW implementation matrix of fractional integration [2,17]. Using (43) and (44), we have…”

Section: Definition 1 the Riemann-liouville Fractional Integral Opermentioning

confidence: 99%

“…Numerical strategies for the SNVIE are spline collocation methods [3], Newton-Cotes methods [4], extrapolation algorithm [5], and Hermite-collocation method [6]. The most popular methods for talking about the such equations are introduced, such as homotopy asymptotic method [7], Nyström interpolant method [8], Mesh method [9], Tau method [10], Laplace transform [11], orthonormal Bernstein, and block-pulse functions [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

Ali

Mousa

2019

Advances in Mathematical Physics

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We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage.

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A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

Ali

2019

SN Appl. Sci.

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Hybrid orthonormal Bernstein and block-pulse function wavelet method for many phenomena in mathematical physics and astrophysics is considered. We use a fundamental administrator and convert Lane-Emden conditions into necessary conditions. The upsides of utilizing the proposed strategy are introduced. At that point, an effective error estimation for the proposed technique is additionally presented lastly a few examinations and their numerical arrangements are given; and looking at between the numerical outcomes acquired from alternate strategies, we demonstrate the high exactness and productivity of the proposed strategy. Our method is characterized then the singular equations are transformed to Volterra integro-differential equations. We modify this equations to an algebraic system of equations. The solution to this application is achieved by solving this system and the constructed solutions are on approximation form. The acquired results guarantee the method provides a truncate solution to the Lane-Emden equations.

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Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

Cited by 12 publications

References 16 publications

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

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