Exact solutions for nonlinear evolution equations using novel test function

Singh, Manjit; Gupta, Rajesh Kumar

doi:10.1007/s11071-016-2955-2

Cited by 11 publications

(3 citation statements)

References 25 publications

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“…The bilinear equations and , obtained earlier, have been considered to construct exact solutions of Equations and by taking the following test function:

\begin{matrix} right & left ϕ = e^{- ξ_{1}} + δ_{1} \tan (ξ_{2}) + δ_{2} \tanh (ξ_{3}) + δ_{3} e^{ξ_{1}}, & right \\ right & left where ξ_{j} = a_{j} x + b_{j} y + c_{j} t + e_{j} z, j = 1, 2, 3 . \end{matrix}

On substitution of into bilinear equations and , collection of the coefficients of

e^{\pm ξ_{1}}, e^{\pm ξ_{1}} \tan false(ξ_{2} false), e^{\pm ξ_{1}} \tanh false(ξ_{3} false), \tan false(ξ_{2} false) \tanh false(ξ_{3} false)

and thereafter, setting each coefficient to zero yield a set of overdetermined algebraic equations. Various types of solutions are derived on solving these set of equations, which are listed in the following sections.…”

Section: Explicit Solutions For Extended (3 + 1)‐dimensional Jimbo‐mimentioning

confidence: 99%

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New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

Kaur

Wazwaz

2018

Math Methods in App Sciences

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In this work, we investigate extended (3 + 1)‐dimensional Jimbo‐Miwa equations by locating movable critical points with the aid of Painlevé analysis. We construct bilinear forms through using truncated Painlevé expansions along with the Bell polynomials approach. The proposed approach provides enough freedom to construct solutions that may be related to large variety of real physical phenomena, and in addition, this approach enriches the solution structure. Abundant exact solutions involving various arbitrary constants are furnished in uniform manner by using test function. The obtained solutions are entirely new and different from those reported in the literature.

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“…The bilinear equations and , obtained earlier, have been considered to construct exact solutions of Equations and by taking the following test function:

\begin{matrix} right & left ϕ = e^{- ξ_{1}} + δ_{1} \tan (ξ_{2}) + δ_{2} \tanh (ξ_{3}) + δ_{3} e^{ξ_{1}}, & right \\ right & left where ξ_{j} = a_{j} x + b_{j} y + c_{j} t + e_{j} z, j = 1, 2, 3 . \end{matrix}

On substitution of into bilinear equations and , collection of the coefficients of

e^{\pm ξ_{1}}, e^{\pm ξ_{1}} \tan false(ξ_{2} false), e^{\pm ξ_{1}} \tanh false(ξ_{3} false), \tan false(ξ_{2} false) \tanh false(ξ_{3} false)

Section: Explicit Solutions For Extended (3 + 1)‐dimensional Jimbo‐mimentioning

confidence: 99%

“…The bilinear equations (3.9) and (3.11), obtained earlier, have been considered to construct exact solutions of Equations 1.2 and 1.3 by taking the following test function 29 :…”

Section: Explicit Solutions For Extended (3 + 1)-dimensional Jimbo-mentioning

confidence: 99%

New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

Kaur

Wazwaz

2018

Math Methods in App Sciences

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“…tic function method [12][13][14], the tanh-function method [15,16], the (G ' /G)-expansion method [17][18][19][20][21][22], the modified simple equation method [23][24][25][26], the Kudryashov method [27][28][29], the multiple exp-function algorithm method [30,31], the transformed rational function method [32], the Frobenius decomposition technique [33], the local fractional variation iteration method [34], the local fractional series expansion method [35], the (G ' /G, 1/G)-expansion method [36][37][38][39][40], the generalized Riccati equation mapping method [41][42][43], the test function method [44,45] and so on.…”

Section: Mathematics Subject Classification: 35k99 35p05 35p99 35c05mentioning

confidence: 99%

Untitled

2017

Int J Opt Photonic Eng

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The investigation of exact traveling wave solutions to nonlinear PDEs plays an important role in the study of nonlinear physical phenomena. Nonlinear wave phenomena appears in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, biology, solid state physics, chemical kinematics, chemical physics and geochemistry. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent decades, many effective methods have been established to obtain exact solutions of nonlinear PDEs, such as the inverse scattering transform [1], the Hirota method [2], the truncated Painlevé expansion method [3], the Bäcklund transform method [1,4-8], the simplest equation method [9,10], the Weierstrass elliptic function method [11], the Jacobi ellip

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Nonclassical symmetries and similarity solutions of variable coefficient coupled KdV system using compatibility method

Gupta

Singh

2016

Nonlinear Dyn

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Exact solutions for nonlinear evolution equations using novel test function

Cited by 11 publications

References 25 publications

New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

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Nonclassical symmetries and similarity solutions of variable coefficient coupled KdV system using compatibility method

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