New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method

[1] Peregrine D.H., Calculations of the development of an undular bore, Journal of Fluid Mechanics, 25(2), 321–300, 1966. PeregrineD.H. Calculations of the development of an undular bore Journal of Fluid Mechanics 25 2 321 300 1966 Search in Google Scholar

[2] Benjamin T.B., Bona J.L., Mahony J.J., Model equations for long waves in nonlinear dispersive systems, Philosophical Transactions of the Royal Society A, Mathematical, Physical and Engineering Sciences, 272(1220), 47–78, 1972. BenjaminT.B. BonaJ.L. MahonyJ.J. Model equations for long waves in nonlinear dispersive systems Philosophical Transactions of the Royal Society A, Mathematical, Physical and Engineering Sciences 272 1220 47 78 1972 Search in Google Scholar

[3] Usman M., Hussain A., Zaman F.D., Khan I., Eldin S.M., Reciprocal Bäcklund transformations and travelling wave structures of some nonlinear pseudo-parabolic equations, Partial Differential Equations in Applied Mathematics, 7, 100490, 2023. UsmanM. HussainA. ZamanF.D. KhanI. EldinS.M. Reciprocal Bäcklund transformations and travelling wave structures of some nonlinear pseudo-parabolic equations Partial Differential Equations in Applied Mathematics 7 100490 2023 Search in Google Scholar

[4] Rehman S., Hussain A., Rahman J.U., Anjum N., Munir T., Modified laplace based variational iteration method for the mechanical vibrations and its applications, Acta Mechanica et Automatica, 16(2), 98–102, 2022. RehmanS. HussainA. RahmanJ.U. AnjumN. MunirT. Modified laplace based variational iteration method for the mechanical vibrations and its applications Acta Mechanica et Automatica 16 2 98 102 2022 Search in Google Scholar

[5] Oskolkov A., Nonlocal problems for one class of nonlinear operator equations that arise in the theory of sobolev type equations, Journal of Soviet Mathematics, 64(1), 724–735, 1993. OskolkovA. Nonlocal problems for one class of nonlinear operator equations that arise in the theory of sobolev type equations Journal of Soviet Mathematics 64 1 724 735 1993 Search in Google Scholar

[6] Rani S., Kumar S., Mann N., On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods, Optical and Quantum Electronics, 55, 731, 2023. RaniS. KumarS. MannN. On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods Optical and Quantum Electronics 55 731 2023 Search in Google Scholar

[7] Kumar S., Mohan B., Kumar R., Newly formed center-controlled rouge wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach, Physica Scripta, 98(8), 085237, 2023. KumarS. MohanB. KumarR. Newly formed center-controlled rouge wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach Physica Scripta 98 8 085237 2023 Search in Google Scholar

[8] Kumar A., Kumar S., Kharbanda H., Closed-form invariant solutions from the Lie symmetry analysis and dynamics of solitonic profiles for (2+1)-dimensional modified Heisenberg ferromagnetic system, Modern Physics Letters B, 36(07), 2150609, 2022. KumarA. KumarS. KharbandaH. Closed-form invariant solutions from the Lie symmetry analysis and dynamics of solitonic profiles for (2+1)-dimensional modified Heisenberg ferromagnetic system Modern Physics Letters B 36 07 2150609 2022 Search in Google Scholar

[9] Oskolkov A.P., On stability theory for solutions of semilinear dissipative equations of the Sobolev type, Journal of Mathematical Sciences, 77, 3225–3231, 1995. OskolkovA.P. On stability theory for solutions of semilinear dissipative equations of the Sobolev type Journal of Mathematical Sciences 77 3225 3231 1995 Search in Google Scholar

[10] Camassa R., Holm D.D., An integrable shallow water equation with peaked solitons, Physical Review Letters, 71(11), 1661–1664, 1993. CamassaR. HolmD.D. An integrable shallow water equation with peaked solitons Physical Review Letters 71 11 1661 1664 1993 Search in Google Scholar

[11] Camassa R., Holm D.D., Hyman J.M., A new integrable shallow water equation, Advances in Applied Mechanics, 31, 1–33, 1994. CamassaR. HolmD.D. HymanJ.M. A new integrable shallow water equation Advances in Applied Mechanics 31 1 33 1994 Search in Google Scholar

[12] Johnson R.S., Camassa-Holm, Korteweg-de Vries and related models for water waves, Journal of Fluid Mechanics, 455, 63–82, 2002. JohnsonR.S. Camassa-Holm, Korteweg-de Vries and related models for water waves Journal of Fluid Mechanics 455 63 82 2002 Search in Google Scholar

[13] Amfilokhiev V.B., Pavlovskii V.A., Mazaeva N.P., Khodorkovskii Y.S., Flows of polymer solutions in the presence of convective accelerations, Trudy Leningrad. Korablestr. Inst. 96, 3–9, 1975. AmfilokhievV.B. PavlovskiiV.A. MazaevaN.P. KhodorkovskiiY.S. Flows of polymer solutions in the presence of convective accelerations Trudy Leningrad. Korablestr. Inst. 96 3 9 1975 Search in Google Scholar

[14] Wazwaz A.M., New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations, Applied Mathematics and Computation, 186(1), 130–141, 2007. WazwazA.M. New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations Applied Mathematics and Computation 186 1 130 141 2007 Search in Google Scholar

[15] Whitham G.B., Variational methods and applications to water waves, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 299(1456), 6–25, 1967. WhithamG.B. Variational methods and applications to water waves Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 299 1456 6 25 1967 Search in Google Scholar

[16] Fornberg B., Whitham G.B., A numerical and theoretical study of certain nonlinear wave phenomena, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 289(1361), 373–404, 1978. FornbergB. WhithamG.B. A numerical and theoretical study of certain nonlinear wave phenomena Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 289 1361 373 404 1978 Search in Google Scholar

[17] Hussain A., Kara A.H., Zaman F.D., An invariance analysis of the Vakhnenko-Parkes equation, Chaos Solitons Fractals, 171, 113423, 2023. HussainA. KaraA.H. ZamanF.D. An invariance analysis of the Vakhnenko-Parkes equation Chaos Solitons Fractals 171 113423 2023 Search in Google Scholar

[18] Hussain A., Usman M., Zaman F.D., Eldin S.M., Symmetry analysis and invariant solutions of Riabouchinsky Proudman Johnson equation using optimal system of Lie subalgebras, Results in Physics, 49, 106507, 2023. HussainA. UsmanM. ZamanF.D. EldinS.M. Symmetry analysis and invariant solutions of Riabouchinsky Proudman Johnson equation using optimal system of Lie subalgebras Results in Physics 49 106507 2023 Search in Google Scholar

[19] Hussain A., Usman M., Al-Sinan B.R., Osman W.M., Ibrahim T.F., Symmetry analysis and closed-form invariant solutions of the non-linear wave equations in elasticity using optimal system of Lie subalgebra, Chinese Journal of Physics, 83(1), 1–13, 2023. HussainA. UsmanM. Al-SinanB.R. OsmanW.M. IbrahimT.F. Symmetry analysis and closed-form invariant solutions of the non-linear wave equations in elasticity using optimal system of Lie subalgebra Chinese Journal of Physics 83 1 1 13 2023 Search in Google Scholar

[20] Usman M., Hussain A., Zaman F.D., Eldin S.M., Group invariant solutions of wave propagation in phononic materials based on the reduced micromorphic model via optimal system of Lie subalgebra, Results in Physics, 48, 106413, 2023. UsmanM. HussainA. ZamanF.D. EldinS.M. Group invariant solutions of wave propagation in phononic materials based on the reduced micromorphic model via optimal system of Lie subalgebra Results in Physics 48 106413 2023 Search in Google Scholar

[21] Hussain A., Usman M., Zaman F.D., Eldin S.M., Double reductions and traveling wave structures of the generalized Pochhammer-Chree equation, Partial Differential Equations in Applied Mathematics, 7, 100521, 2023. HussainA. UsmanM. ZamanF.D. EldinS.M. Double reductions and traveling wave structures of the generalized Pochhammer-Chree equation Partial Differential Equations in Applied Mathematics 7 100521 2023 Search in Google Scholar

[22] Hussain A., Usman M., Zaman F.D., Ibrahim T.F., Dawood A.A., Symmetry analysis, closed-form invariant solutions and dynamical wave structures of the Benney-Luke equation using optimal system of Lie subalgebras, Chinese Journal of Physics, 84, 66–88, 2023. HussainA. UsmanM. ZamanF.D. IbrahimT.F. DawoodA.A. Symmetry analysis, closed-form invariant solutions and dynamical wave structures of the Benney-Luke equation using optimal system of Lie subalgebras Chinese Journal of Physics 84 66 88 2023 Search in Google Scholar

[23] Hussain A., Usman M., Zaman F.D., Eldin S.M., Optical solitons with DNA dynamics arising in oscillator-chain of Peyrard-Bishop model, Results in Physics, 50, 106586, 2023. HussainA. UsmanM. ZamanF.D. EldinS.M. Optical solitons with DNA dynamics arising in oscillator-chain of Peyrard-Bishop model Results in Physics 50 106586 2023 Search in Google Scholar

[24] Usman M., Hussain A., Zaman F.D., Eldin S.M., Symmetry analysis and exact Jacobi elliptic solutions for the nonlinear couple Drinfeld Sokolov Wilson dynamical system arising in shallow water waves, Results in Physics, 51, 106613, 2023. UsmanM. HussainA. ZamanF.D. EldinS.M. Symmetry analysis and exact Jacobi elliptic solutions for the nonlinear couple Drinfeld Sokolov Wilson dynamical system arising in shallow water waves Results in Physics 51 106613 2023 Search in Google Scholar

[25] Hussain A., Kara A.H., Zaman F.D., Symmetries, associated first integrals and successive reduction of Schrödinger type and other second order difference equations, Optik, 287, 171080, 2023. HussainA. KaraA.H. ZamanF.D. Symmetries, associated first integrals and successive reduction of Schrödinger type and other second order difference equations Optik 287 171080 2023 Search in Google Scholar

[26] Usman M., Hussain A., Zaman F.D., Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets, Physica Scripta, 98(9), 095205, 2023. UsmanM. HussainA. ZamanF.D. Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets Physica Scripta 98 9 095205 2023 Search in Google Scholar

[27] Akcagil S., Aydemir T., Gozukizil O.F., Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the G′/G-expansion method, New Trends in Mathematical Sciences, 4(4), 51–66, 2016. AkcagilS. AydemirT. GozukizilO.F. Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the G′/G-expansion method New Trends in Mathematical Sciences 4 4 51 66 2016 Search in Google Scholar

[28] Rezazadeh H., New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity, Optik, 167, 218–227, 2018. RezazadehH. New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity Optik 167 218 227 2018 Search in Google Scholar

[29] Gözükızıl Ö.F., Akçağıl Ş., The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions, Advances in Difference Equations, 2013(143), 1–18, 2013. GözükızılÖ.F. AkçağılŞ. The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions Advances in Difference Equations 2013 143 1 18 2013 Search in Google Scholar