The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytica...The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytical solutions for the system.The invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry approach.The invariant solutions involve time,space variables,and arbitrary constants.Imposing adequate constraints on arbitrary constants,solutions are represented graphically to make them more applicable in designing sea models.The behavior of solutions shows asymptotic,bell-shaped,bright and dark soliton,bright soliton,parabolic,bright and kink,kink,and periodic nature.The constructed results are novel as the reported results[26,28,29,30,33,38,42,49]can be deduced from the results derived in this study.The remaining solutions derived in this study,are absolutely different from the earlier findings.In this study,the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.展开更多
This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or i...This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or in wide channels.The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory.The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs.Under adequate restrictions,the reduced system of ODEs is solved.Numerical simulation is performed to describe the solutions in a physically meaningful way.The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein.In each animation,a frame for dominated behavior is captured.They exhibit elastic multisolitons,single soliton,doubly solitons,stationary,kink and parabolic nature.The results are significant since these have confirmed some of the established results of S.Kumar et al.(2020)and K.Sharma et al.(2020).Some of their solutions can be deduced from the results derived in this work.Other results in the existing literature are different from those in this work.展开更多
文摘The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytical solutions for the system.The invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry approach.The invariant solutions involve time,space variables,and arbitrary constants.Imposing adequate constraints on arbitrary constants,solutions are represented graphically to make them more applicable in designing sea models.The behavior of solutions shows asymptotic,bell-shaped,bright and dark soliton,bright soliton,parabolic,bright and kink,kink,and periodic nature.The constructed results are novel as the reported results[26,28,29,30,33,38,42,49]can be deduced from the results derived in this study.The remaining solutions derived in this study,are absolutely different from the earlier findings.In this study,the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.
文摘This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or in wide channels.The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory.The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs.Under adequate restrictions,the reduced system of ODEs is solved.Numerical simulation is performed to describe the solutions in a physically meaningful way.The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein.In each animation,a frame for dominated behavior is captured.They exhibit elastic multisolitons,single soliton,doubly solitons,stationary,kink and parabolic nature.The results are significant since these have confirmed some of the established results of S.Kumar et al.(2020)and K.Sharma et al.(2020).Some of their solutions can be deduced from the results derived in this work.Other results in the existing literature are different from those in this work.
