Division theorem combined with the Riccati equation for solving some nonlinear Schrödinger-like equations

Lü, Bin

doi:10.1016/j.amc.2012.08.009

Cited by 2 publications

(7 citation statements)

References 24 publications

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“…Locking for our result and Lu's results [15] Eq. (55) to (62), we found the same result it means these methods have similar solutions.…”

Section: Coupled Higher Order Nonlinear Schrödinger Equationmentioning

confidence: 59%

“…The -expansion method is applied to solve the coupled higher order nonlinear Schrödinger equation successfully obtained the exact solution, and compared the result with first integral method [15] and coupled phaseamplitude formulation [13]. Our method provides not only more general forms of solutions (the hyperbolic, the trigonometric and rational function solutions), but also periodic and solitary wave solutions.…”

Section: Resultsmentioning

confidence: 98%

“…(17a), (17b), (19a) and (19b) by coupled phase-amplitude formulation the same our solutions. Lu [15] solutions Eq. (55)-(62), also, the same our solutions.…”

Section: Resultsmentioning

confidence: 99%

“…(14), we can suppose that the solution of (ODE) is of the form. (15) and are constants to be determined later, substituting -expansion method (15) into the left hand side of Eq.…”

Section: Coupled Higher Order Nonlinear Schrödinger Equationmentioning

confidence: 99%

“…Bin Lu [15] used first integral method to exact solitary wave solutions for arbitrary nonlinear parameters. Considered by Sasa and Satsuma [16].…”

Section: Introductionmentioning

confidence: 99%

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Explicit solutions for couple higher order nonlinear Schrödinger equation by (G′G)-expansion method

Taha

Noorani²

2013

AIP Conference Proceedings

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The G G ' -expansion method is used to study coupled higher order nonlinear Schrödinger equation. The traveling wave solutions obtained via this method are expressed by hyperbolic functions and the trigonometric functions. In addition to solitary waves solutions and periodic obtained when the choice of parameters are taken at special values. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.

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“…Locking for our result and Lu's results [15] Eq. (55) to (62), we found the same result it means these methods have similar solutions.…”

Section: Coupled Higher Order Nonlinear Schrödinger Equationmentioning

confidence: 59%

Section: Resultsmentioning

confidence: 98%

“…(17a), (17b), (19a) and (19b) by coupled phase-amplitude formulation the same our solutions. Lu [15] solutions Eq. (55)-(62), also, the same our solutions.…”

Section: Resultsmentioning

confidence: 99%

“…(14), we can suppose that the solution of (ODE) is of the form. (15) and are constants to be determined later, substituting -expansion method (15) into the left hand side of Eq.…”

Section: Coupled Higher Order Nonlinear Schrödinger Equationmentioning

confidence: 99%

“…Bin Lu [15] used first integral method to exact solitary wave solutions for arbitrary nonlinear parameters. Considered by Sasa and Satsuma [16].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Explicit solutions for couple higher order nonlinear Schrödinger equation by (G′G)-expansion method

Taha

Noorani²

2013

AIP Conference Proceedings

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Construction of New Infinite-Series Exact Solitary Wave Solutions and Its Application to the Korteweg–De Vries Equation

Guo

2023

Fractal Fract

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The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying these topics. In the present paper, using distinct function iteration relations in two ways, namely, squaring infinitely and extracting the square root infinitely, which have not been reported in other documents, we construct abundant types of new infinite-series exact solitary wave solutions using the auxiliary equation method. Most of these solutions have not been reported in previous papers. The numerical analysis of some solutions shows complex solitary wave phenomena. Some solutions can have stable solitary wave structures, while others may have singularities in certain space–time positions. The results show that the analysis model we use is very simple and effective for the construction of new infinite-series solutions and new solitary wave structures of nonlinear models.

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Division theorem combined with the Riccati equation for solving some nonlinear Schrödinger-like equations

Cited by 2 publications

References 24 publications

Explicit solutions for couple higher order nonlinear Schrödinger equation by (G′G)-expansion method

Explicit solutions for couple higher order nonlinear Schrödinger equation by (G′G)-expansion method

Construction of New Infinite-Series Exact Solitary Wave Solutions and Its Application to the Korteweg–De Vries Equation

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