By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.
We study peaked wave solutions of a generalized Hyperelastic-rod wave equation describing waves in compressible hyperelastic-rods by using the bifurcation theory of planar dynamical systems and numerical simulation me...We study peaked wave solutions of a generalized Hyperelastic-rod wave equation describing waves in compressible hyperelastic-rods by using the bifurcation theory of planar dynamical systems and numerical simulation method. The existence domain of the peaked solitary waves are found. The analytic expressions of peaked solitary wave solutions are obtained. Our numerical simulation and qualitative results are identical.展开更多
Effects of currents on winter wind waves in the tide-dominated Qiongzhou Strait(QS)were numerically evaluated via employing the coupled ocean-atmosphere-wave-sediment transport(COAWST)modeling system.Validations showe...Effects of currents on winter wind waves in the tide-dominated Qiongzhou Strait(QS)were numerically evaluated via employing the coupled ocean-atmosphere-wave-sediment transport(COAWST)modeling system.Validations showed satisfactory model performance in simulating the intense tidal currents in the QS.Different effects of sea level variations and tidal currents on waves were examined under the maximum eastward(METC)and westward(MWTC)tidal currents.In the east entrance area of the QS,the positive sea levels under the MWTC deepened the water depth felt by waves,benefiting the further propagation of wave energy into the inner strait and causing increased wave height.The METC and the MWTC could both enhance the wave height in the east entrance area of the QS,mainly through current-induced convergence and wavenumber shift,respectively.By current-induced refraction,the METC(MWTC)triggered counterclockwise(clockwise)rotation in peak wave directions in the northern part of the QS while clockwise(counterclockwise)rotation in the southern part.展开更多
By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are al...By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented.展开更多
We use qualitative analysis and numerical simulation to study peaked traveling wave solutions of CH-γ and CH equations. General expressions of peakon and periodic cusp wave solutions are obtained. Some previous resul...We use qualitative analysis and numerical simulation to study peaked traveling wave solutions of CH-γ and CH equations. General expressions of peakon and periodic cusp wave solutions are obtained. Some previous results become our special cases.展开更多
The Degasperis-Procesi （DP） equation describing the propagation of shallow water waves contains a physical parameter co, and it is well-known that the DP equation admits solitary waves with a peaked crest when ω = ...The Degasperis-Procesi （DP） equation describing the propagation of shallow water waves contains a physical parameter co, and it is well-known that the DP equation admits solitary waves with a peaked crest when ω = 0. In this article, we illustrate, for the first time, that the DP equation admits peaked solitary waves even when ω≠ 0. This is helpful to enrich our knowledge and deepen our understandings about peaked solitary waves of the DP equation.展开更多
The propagation of waves in shallow waters is affected by the bottom topography unlike deep water waves of the coastal environment.Due to the interaction of the wave with bed topography,the wave transformation process...The propagation of waves in shallow waters is affected by the bottom topography unlike deep water waves of the coastal environment.Due to the interaction of the wave with bed topography,the wave transformation processes occur.Refraction,diffraction,shoaling,and breaking are the wave transforma-tion processes that occur in the coastal environment.The significant wave height over rugged topography is a standardized statistics to denote the characteristic height of the random waves in a sea state.There-fore,the objective of the present study is to predict the significant wave height over rugged topography.The SWAN standalone and SWAN DHH platform are used to predict significant wave height over rugged topography in Mehamn harbour,Norway.The SWAN model results are almost similar to the lab data of Vold and Lothe(2009)for all the 22 scenarios at all the output locations.Further,the four cases reported by Taehun(2011)and lab data from Vold and Lothe(2009)for that four cases are compared with the SWAN model results.It is observed that the SWAN model results are much closer to the lab data of Vold and Lothe(2009).展开更多
In this paper,we investigate the orbital stability of the peaked solitons(peakons)for the modified Camassa–Holm equation with cubic nonlinearity.We consider a minimization problem with an appropriately chosen constra...In this paper,we investigate the orbital stability of the peaked solitons(peakons)for the modified Camassa–Holm equation with cubic nonlinearity.We consider a minimization problem with an appropriately chosen constraint,from which we establish the orbital stability of the peakons under H^(1)∩W^(1,4)norm.展开更多
In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by re...In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.展开更多
基金Supported by the Nature Science Foundation of Shandong (No. 2004zx16,Q2005A01)
文摘By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.
基金This research was supported by National Natural Science Foundation of China (10571062)Natural Science Foundation of Yunnan (6Y147A).
文摘We study peaked wave solutions of a generalized Hyperelastic-rod wave equation describing waves in compressible hyperelastic-rods by using the bifurcation theory of planar dynamical systems and numerical simulation method. The existence domain of the peaked solitary waves are found. The analytic expressions of peaked solitary wave solutions are obtained. Our numerical simulation and qualitative results are identical.
基金The Fund of Southern Marine Science and Engineering Guangdong Laboratory(Zhanjiang)under contract No.ZJW-2019-08the Program for Scientific Research Start-up Funds of Guangdong Ocean University under contract No.101302/R18001+1 种基金the National Natural Science Foundation of China under contract No.41776034the First-class Discipline Plan of Guangdong Province under contract No.CYL231419012。
文摘Effects of currents on winter wind waves in the tide-dominated Qiongzhou Strait(QS)were numerically evaluated via employing the coupled ocean-atmosphere-wave-sediment transport(COAWST)modeling system.Validations showed satisfactory model performance in simulating the intense tidal currents in the QS.Different effects of sea level variations and tidal currents on waves were examined under the maximum eastward(METC)and westward(MWTC)tidal currents.In the east entrance area of the QS,the positive sea levels under the MWTC deepened the water depth felt by waves,benefiting the further propagation of wave energy into the inner strait and causing increased wave height.The METC and the MWTC could both enhance the wave height in the east entrance area of the QS,mainly through current-induced convergence and wavenumber shift,respectively.By current-induced refraction,the METC(MWTC)triggered counterclockwise(clockwise)rotation in peak wave directions in the northern part of the QS while clockwise(counterclockwise)rotation in the southern part.
基金Supported by National Nature Science Foundation of China under Grant No.11102076Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant No.15KJB110005
文摘By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented.
文摘We use qualitative analysis and numerical simulation to study peaked traveling wave solutions of CH-γ and CH equations. General expressions of peakon and periodic cusp wave solutions are obtained. Some previous results become our special cases.
基金supported by the State Key Lab of Ocean Engineering(Grant No. GKZD010056-6)the National Natural Science Foundation of China (Grant No. 11272209)
文摘The Degasperis-Procesi （DP） equation describing the propagation of shallow water waves contains a physical parameter co, and it is well-known that the DP equation admits solitary waves with a peaked crest when ω = 0. In this article, we illustrate, for the first time, that the DP equation admits peaked solitary waves even when ω≠ 0. This is helpful to enrich our knowledge and deepen our understandings about peaked solitary waves of the DP equation.
文摘The propagation of waves in shallow waters is affected by the bottom topography unlike deep water waves of the coastal environment.Due to the interaction of the wave with bed topography,the wave transformation processes occur.Refraction,diffraction,shoaling,and breaking are the wave transforma-tion processes that occur in the coastal environment.The significant wave height over rugged topography is a standardized statistics to denote the characteristic height of the random waves in a sea state.There-fore,the objective of the present study is to predict the significant wave height over rugged topography.The SWAN standalone and SWAN DHH platform are used to predict significant wave height over rugged topography in Mehamn harbour,Norway.The SWAN model results are almost similar to the lab data of Vold and Lothe(2009)for all the 22 scenarios at all the output locations.Further,the four cases reported by Taehun(2011)and lab data from Vold and Lothe(2009)for that four cases are compared with the SWAN model results.It is observed that the SWAN model results are much closer to the lab data of Vold and Lothe(2009).
文摘In this paper,we investigate the orbital stability of the peaked solitons(peakons)for the modified Camassa–Holm equation with cubic nonlinearity.We consider a minimization problem with an appropriately chosen constraint,from which we establish the orbital stability of the peakons under H^(1)∩W^(1,4)norm.
基金Supported by National Natural Science Foundation of China under Grant No.11471174NSF of Ningbo under Grant No.2014A610018
文摘In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.
