By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala...A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.展开更多
Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear...Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.展开更多
In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification...In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.展开更多
The Antarctic Circumpolar Current (ACC) and its associated Meridional Overturning Circulation (MOC) is investigated through a nonlinear inertia theory model, which consists of two layers--an upper Ekman layer driven m...The Antarctic Circumpolar Current (ACC) and its associated Meridional Overturning Circulation (MOC) is investigated through a nonlinear inertia theory model, which consists of two layers--an upper Ekman layer driven mainly by sea surface wind stress and a lower thermocline controlled by ideal fluid nonlinear equations which can be solved by identifying the form of the arbitrary functions. The results show that the thermocline has a two-equilibrium solution though given the same Ekman layer condition. Compared to the first equilibrium, the second one has a heavier intensity and deeper circulation, which seems more consistent with the existing data.展开更多
Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-di...Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells.A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains.Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation,and their stabilities are determined via the modified sorting method.The effects of excitations on the steady-state responses are analyzed.The results reveal a crucial role played by the phase difference in the structural response,and the phase difference can effectively control the amplitude of vibration.展开更多
文摘By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
基金Supported by the National Natural Science Foundation of China under Grant No. 11071209the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province under Grant No. 10KJBll0011
文摘A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10672141, 10732020, and 11072008)
文摘In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.
基金supported by National Basic Research Program of China (Grant No. 2010CB950300)
文摘The Antarctic Circumpolar Current (ACC) and its associated Meridional Overturning Circulation (MOC) is investigated through a nonlinear inertia theory model, which consists of two layers--an upper Ekman layer driven mainly by sea surface wind stress and a lower thermocline controlled by ideal fluid nonlinear equations which can be solved by identifying the form of the arbitrary functions. The results show that the thermocline has a two-equilibrium solution though given the same Ekman layer condition. Compared to the first equilibrium, the second one has a heavier intensity and deeper circulation, which seems more consistent with the existing data.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11672069,11872145,11872159,12172086,and 12101106).
文摘Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells.A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains.Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation,and their stabilities are determined via the modified sorting method.The effects of excitations on the steady-state responses are analyzed.The results reveal a crucial role played by the phase difference in the structural response,and the phase difference can effectively control the amplitude of vibration.
