In this paper,we describe the nonlinear behavior of a generalized fourth-order Hietarinta-type equa-tion for dispersive waves in(2+1)dimension.The various wave formations are retrieved by using Hirota’s bilinear meth...In this paper,we describe the nonlinear behavior of a generalized fourth-order Hietarinta-type equa-tion for dispersive waves in(2+1)dimension.The various wave formations are retrieved by using Hirota’s bilinear method(HBM)and various test function perspectives.The Hirota method is a widely used and robust mathematical tool for finding soliton solutions of nonlinear partial differential equa-tions(NLPDEs)in a variety of disciplines like mathematical physics,nonlinear dynamics,oceanography,engineering sciences,and others requires bilinearization of nonlinear PDEs.The different wave structures in the forms of new breather,lump-periodic,rogue waves,and two-wave solutions are recovered.In addi-tion,the physical behavior of the acquired solutions is illustrated in three-dimensional,two-dimensional,density,and contour profiles by the assistance of suitable parameters.Based on the obtained results,we can assert that the employed methodology is straightforward,dynamic,highly efficient,and will serve as a valuable tool for discussing complex issues in a diversity of domains specifically ocean and coastal engineering.We have also made an important first step in understanding the structure and physical be-havior of complex structures with our findings here.We believe this research is timely and relevant to a wide range of engineering modelers.The results obtained are useful for comprehending the fundamental scenarios of nonlinear sciences.展开更多
The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific...The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.展开更多
基金support provided for this research via Open Fund of State Key Laboratory of Power Grid Environmental Protection (No.GYW51202101374).
文摘In this paper,we describe the nonlinear behavior of a generalized fourth-order Hietarinta-type equa-tion for dispersive waves in(2+1)dimension.The various wave formations are retrieved by using Hirota’s bilinear method(HBM)and various test function perspectives.The Hirota method is a widely used and robust mathematical tool for finding soliton solutions of nonlinear partial differential equa-tions(NLPDEs)in a variety of disciplines like mathematical physics,nonlinear dynamics,oceanography,engineering sciences,and others requires bilinearization of nonlinear PDEs.The different wave structures in the forms of new breather,lump-periodic,rogue waves,and two-wave solutions are recovered.In addi-tion,the physical behavior of the acquired solutions is illustrated in three-dimensional,two-dimensional,density,and contour profiles by the assistance of suitable parameters.Based on the obtained results,we can assert that the employed methodology is straightforward,dynamic,highly efficient,and will serve as a valuable tool for discussing complex issues in a diversity of domains specifically ocean and coastal engineering.We have also made an important first step in understanding the structure and physical be-havior of complex structures with our findings here.We believe this research is timely and relevant to a wide range of engineering modelers.The results obtained are useful for comprehending the fundamental scenarios of nonlinear sciences.
文摘The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.
