For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the metho...For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.展开更多
Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot...Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.展开更多
The nonlinear Schr6dinger equation （NLSE） with variable coefficients in blood vessels is discussed via an NLSE-based constructive method, and exact solutions are obtained including multi-soliton solutions with and w...The nonlinear Schr6dinger equation （NLSE） with variable coefficients in blood vessels is discussed via an NLSE-based constructive method, and exact solutions are obtained including multi-soliton solutions with and without continuous wave backgrounds. The dynamical behaviors of these soliton solutions are studied. The solitonic propagation behaviors such as restraint and sustainment on continuous wave background are discussed by altering the value of dispersion parameter δ. Moreover, the longitude controllable behaviors are also reported by modulating the dispersion parameter ＆ These results are potential1y useful for future experiments in various blood vessels.展开更多
The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are ...The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.展开更多
基金Supported by the Natural Science Foundation of Ningbo under Grant No. 2008A610029
文摘For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030 and 61304133
文摘Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.
基金Supported by the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201225803the National Natural Science Foundation of China under Grant No.11375007+2 种基金the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY13F050006the Student Research Training Program under Grant No.201212007Undergraduate Innovative Base of Zhejiang A&F University
文摘The nonlinear Schr6dinger equation （NLSE） with variable coefficients in blood vessels is discussed via an NLSE-based constructive method, and exact solutions are obtained including multi-soliton solutions with and without continuous wave backgrounds. The dynamical behaviors of these soliton solutions are studied. The solitonic propagation behaviors such as restraint and sustainment on continuous wave background are discussed by altering the value of dispersion parameter δ. Moreover, the longitude controllable behaviors are also reported by modulating the dispersion parameter ＆ These results are potential1y useful for future experiments in various blood vessels.
文摘The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.
