Application of Process Analysis Method to the Solution of 2-DNonlinear Progressive Gravity Waves

1992 ◽  
Vol 36 (01) ◽  
pp. 30-37
Author(s):  
S. J. Liao
Keyword(s):  
Gravity Waves ◽  
Process Analysis ◽  
Perturbation Expansion ◽  
Continuous Mapping ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Analysis Method ◽  
Perturbation Expansion Method

Based on continuous mapping, a kind of analytical method for nonlinear problems, namely, the Process Analysis Method, is described and used to solve two-dimensional nonlinear progressive gravity waves. Solutions at the fourth order of approximation are obtained and compared with Stokesian waves. In contrast to the perturbation expansion method, the Process Analysis Method is independent of small or great parameters and therefore can solve nonlinear problems without small or great parameters.

A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

1992 ◽  
Vol 59 (4) ◽  
pp. 970-975 ◽  
Author(s):  
S. J. Liao
Keyword(s):  
Process Analysis ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Second Order ◽  
Order Of Approximation ◽  
Analysis Method ◽  
Simple Pendulum ◽  
Perturbation Expansion Method ◽  
Second Order Of Approximation ◽  
Perturbation Solutions

In this paper, a new kind of analytical method of nonlinear problem called the process analysis method (PAM) is described and used to give a second-order approximate solution of a simple pendulum. The PAM does not depend on the small parameter supposition and therefore can overcome the disadvantages and limitations of the perturbation expansion method. The analytical approximate results at the second-order of approximation are in good agreement with the numerical results. They are compared with perturbation solutions, and it appears that even the firstorder solutions are more accurate than the perturbation solutions at second-order of approximation.

A Perturbation Expansion Method to Study Highly Correlated Spins

2009 ◽  
Vol 23 (1) ◽  
pp. 145-148
Author(s):  
E. V. Anda ◽  
G. Chiappe ◽  
C. A. Büsser ◽  
M. A. Davidovich ◽  
G. B. Martins ◽  
...  
Keyword(s):  
Perturbation Expansion ◽  
Expansion Method ◽  
Highly Correlated ◽  
Perturbation Expansion Method

Long waves in a uniform channel of arbitrary cross-section

1968 ◽  
Vol 32 (2) ◽  
pp. 353-365 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Solitary Wave ◽  
Cross Section ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Arbitrary Cross Section ◽  
Long Waves ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Uniform Channel

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Derivation of quantum Chernoff metric with perturbation expansion method

2014 ◽  
Vol 23 (9) ◽  
pp. 090305 ◽  
Author(s):  
Wei Zhong ◽  
Jian Ma ◽  
Jing Liu ◽  
Xiao-Guang Wang
Keyword(s):  
Perturbation Expansion ◽  
Expansion Method ◽  
Perturbation Expansion Method

Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

1998 ◽  
Vol 60 (1) ◽  
pp. 151-158 ◽  
Author(s):  
DEBALINA CHAKRABORTY ◽  
K. P. DAS
Keyword(s):  
Acoustic Waves ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Petviashvili Equation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
The Stability ◽  
Perturbation Expansion Method

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

GABITOV–TURITSYN EQUATION FOR SOLITONS IN OPTICAL FIBERS

2003 ◽  
Vol 12 (01) ◽  
pp. 17-37 ◽  
Author(s):  
ANJAN BISWAS
Keyword(s):  
Optical Fibers ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Multiple Scale ◽  
Optical Solitons ◽  
Dispersion Management ◽  
Wavelength Division ◽  
Wavelength Division Multiplexed ◽  
Scale Perturbation ◽  
Perturbation Expansion Method

The dynamics of optical solitons with dispersion-management propagating through optical fibers with damping and amplification is studied. A multiple-scale perturbation expansion method is used to analyze the nonlinear Schrödinger's equation that governs the propagation of such solitons. In this paper we have considered both polarization preserving as well as birefringent fibers. Finally, the case of dense wavelength-division-multiplexed soliton system is also considered.

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