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Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics
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作者 Jalil Manafian Onur Alp Ilhan +1 位作者 As’ad Alizadeh Sizar Abid Mohammed 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第7期8-20,共13页
The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK)equation.The solutions obtained contain first-order,second-orde... The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK)equation.The solutions obtained contain first-order,second-order,and third-order wave solutions.At the critical point,the second-order derivative and Hessian matrix for only one point is investigated,and the lump solution has one maximum value.He’s semi-inverse variational principle(SIVP)is also used for the generalized BK equation.Three major cases are studied,based on two different ansatzes using the SIVP.The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below,using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer,fluid dynamics,etc. 展开更多
关键词 multiple rogue wave solutions multiple soliton solutions generalized Bogoyavlensky–Konopelchenko equation semi-inverse variational principle
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Multiple-order line rogue wave,lump and its interaction,periodic,and cross-kink solutions for the generalized CHKP equation
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作者 Yufeng Qian Jalil Manafian +3 位作者 Sherin Youns Mohyaldeen Liqaa S.Esmail Sergey Alekseevich Gorovoy Gurpreet Singh 《Propulsion and Power Research》 SCIE 2021年第3期277-293,共17页
The multiple-order line rogue wave solutions method is emp loyed for searching the multiple soliton solutions for the generalized(2+1)-dimensional Camassa-HolmKadomtsev-Petviashvili(CHKP)equation,which contains first-... The multiple-order line rogue wave solutions method is emp loyed for searching the multiple soliton solutions for the generalized(2+1)-dimensional Camassa-HolmKadomtsev-Petviashvili(CHKP)equation,which contains first-order,second-order,and third-order waves solutions.At the critical point,the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one minimum value.For the case,the lump solution will be shown the bright-dark lump structure and for another case can be present the dark lump structure-two small peaks and one deep hole.Also,the interaction of lump with periodic waves and the interaction between lump and soliton can be obtained by introducing the Hirota forms.In the meanwhile,the cross-kink wave and periodic wave solutions can be gained by the Hirota operator.The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values.We alternative offer that the determining method is general,impressive,outspoken,and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering. 展开更多
关键词 multiple rogue wave solutions multiple soliton solutions Generalized CamassaHolm-KadomtsevPetviashvili equation Lump solution Hirota operator
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