GLOBAL EXISTENCE FOR THE NONHOMOGENEOUS QUASILINEAR WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS

It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.

(2+1)-dimensional dissipation nonlinear Schrdinger equatio for envelope Rossby solitary waves and chirp effect

In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.

Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation.The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures （RAS）.The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes,proximal in time but distant in space,may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors.The space-time distribution of coupled MLH ＞ 5.5 events has been stable for the period of instrumental seismicity,with the largest events occurring in pairs,one shortly after another,on two ends of the rift system and with couples of smaller events in the central part of the rift.The event couples appear as peaks of earthquake ‘migration＇ rate with an approximately decadal periodicity.Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation.The new knowledge,with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis,may be of theoretical and practical value for earthquake prediction issues.Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region,i.e.,there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.

A new finite difference scheme for a dissipative cubic nonlinear Schrdinger equation

This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.

Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations

The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).

Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations

Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.

Quantum Dissipative Threshold and Its Effect on Decay of Metastable State

The coupling between system and reservoir is considered to be linear in the coordinates of the bath but nonlinear in the system's coordinate. A dissipative threshold is observed at finite temperatures due to nonlinear dissipation. The quantum decay rate of a metastable state including higher-order expanded terms of the coupling form function is proposed, which can be strongly decreased at finite temperatures when the quantum dissipative threshold is added to the saddle point of the potential.

NONLINEAR BAROTROPIC INSTABILITY INCLUDING FRICTION DISSIPATION, THERMAL DRIVING AND LARGE TOPOGRAPHY

From a nonlinear quasi-geostrophic barotropic vorticity equation including frictional dissipation, thermal driving and large topography used by Charney in investigation of the multiple flow equilibria and blocking, using the Serrin-Joseph energy method and the variational principle, we found the nonlinear barotropic stability criteria of the zonal basic flow with the total energy, total enstrophy and their linear combination respectively, and compared the criteria with Charney's results.

The Maximum Dissipative Extension of Schrodinger Operator

In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.