scholarly journals Explicit Exact Solution of Damage Probability for Multiple Weapons against a Unitary Target

2016 ◽  
Vol 06 (06) ◽  
pp. 450-467 ◽  
Author(s):  
Hongyun Wang ◽  
Cardy Moten ◽  
Morris Driels ◽  
Don Grundel ◽  
Hong Zhou
Keyword(s):  
Exact Solution ◽  
Damage Probability ◽  
Explicit Exact Solution

EXACT SOLITARY-WAVE SOLUTIONS FOR THE NONLINEAR DISPERSIVE K(2,2,1) and K(3,3,1) EQUATIONS BY THE HOMOTOPY PERTURBATION METHOD

2009 ◽  
Vol 23 (30) ◽  
pp. 3667-3675 ◽  
Author(s):  
AHMET YILDIRIM
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Convergent Series ◽  
Perturbation Series ◽  
Solitary Wave Solutions ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
Explicit Exact Solution

We implemented homotopy perturbation method for approximating the solution to the nonlinear dispersive K(m,n,1) type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the homotopy perturbation series.

Some Nonlinear, Equatorially Trapped, Nonhydrostatic Internal Geophysical Waves

2014 ◽  
Vol 44 (2) ◽  
pp. 781-789 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Exact Solution ◽  
Surface Layer ◽  
Large Amplitude ◽  
Equatorial Waves ◽  
Wind Effects ◽  
Governing Equations ◽  
Near Surface ◽  
Large Amplitude Oscillation ◽  
Geophysical Waves ◽  
Explicit Exact Solution

Abstract The author presents an explicit exact solution to the governing equations for geophysical equatorial waves in the β-plane setting. The solution describes equatorially trapped waves propagating eastward above the thermocline and beneath the near-surface layer where wind effects are confined. At great depths the water is still, while the transition toward the large-amplitude oscillation of the thermocline is accommodated by an eastward-flowing current. Above the thermocline a flow reversal occurs, with the underlying current flowing westward close to the layer where wind effects are confined.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky–Konopelchenko equation by geometric approach

2018 ◽  
Vol 32 (11) ◽  
pp. 1850127 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Exact Solution ◽  
Differential Forms ◽  
Geometric Approach ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariance Group ◽  
Similarity Reduction ◽  
Lie Symmetry Method ◽  
Explicit Exact Solution ◽  
Symmetry Method

In this paper, the symmetry analysis and similarity reduction of the (2[Formula: see text]+[Formula: see text]1)-dimensional Bogoyavlensky–Konopelchenko (B–K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation is obtained.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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