Most of the nonlinear physics systems are essentially nonintegrable. There is no very good analytical approach to solve nonintegrable system. The variable separation approach is a powerful method in linear physics. In...Most of the nonlinear physics systems are essentially nonintegrable. There is no very good analytical approach to solve nonintegrable system. The variable separation approach is a powerful method in linear physics. In this letter, the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation. The method is valid not only for integrable models but also for nonintegrable models. Taking a nonintegrable coupled KdV equation system as a simple example, abundant solitary wave solutions and conoid wave solutions are revealed.展开更多
By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy ＝ 0, λrt - rxx + 2r ∫(qr)xdy ＝ 0, is derived. Some types ...By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy ＝ 0, λrt - rxx + 2r ∫(qr)xdy ＝ 0, is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, farctal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.展开更多
We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable...We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of potential.展开更多
文摘Most of the nonlinear physics systems are essentially nonintegrable. There is no very good analytical approach to solve nonintegrable system. The variable separation approach is a powerful method in linear physics. In this letter, the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation. The method is valid not only for integrable models but also for nonintegrable models. Taking a nonintegrable coupled KdV equation system as a simple example, abundant solitary wave solutions and conoid wave solutions are revealed.
文摘By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy ＝ 0, λrt - rxx + 2r ∫(qr)xdy ＝ 0, is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, farctal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.
文摘We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of potential.
