scholarly journals Stability of Modified Korteweg?de Vries Waves

1987 ◽  
Vol 40 (5) ◽  
pp. 593 ◽  
Author(s):  
K Murawski
Keyword(s):  
Nonlinear Wave ◽  
Stability Criterion ◽  
Wave Theory ◽  
General Stability ◽  
De Vries ◽  
The Stability

A nonlinear wave theory is developed on the basis of the Infeld-Rowlands method to study the stability of modified Korteweg-de Vries waves. A general stability criterion is derived in order to show that unstable waves exist.

On the Stability of Precipitate–Matrix Interfaces in Dilute Ternary Systems

1971 ◽  
Vol 49 (13) ◽  
pp. 1805-1812
Author(s):  
D. E. Coates
Keyword(s):  
Stability Criterion ◽  
Perturbation Methods ◽  
Ternary Systems ◽  
Linear Perturbation ◽  
Matrix Interface ◽  
Interface Stability ◽  
Diffusional Interaction ◽  
General Stability ◽  
The Stability

Using linear perturbation methods, a precipitate–matrix interface stability criterion is obtained for dilute ternary systems. The calculation takes account of capillarity, transport in the precipitate, and ternary diffusional interaction. The general stability criterion contains a term reflecting the destabilizing influence of the solute gradients (i.e., the point effect of diffusion) and a term representing the stabilizing influence of capillarity. Two limiting cases are treated in detail—insignificant transport in the precipitate and negligible ternary diffusional interaction. It is demonstrated that in these two cases the two solutes behave in a cumulative fashion.

scholarly journals The Korteweg-de Vries Equation for Wave Propagation in an Infinitely Long Thin Walled Circular Cylinder Obtained via the Lagrangian Method

1985 ◽  
Vol 40 (9) ◽  
pp. 955-956
Author(s):  
K. Murawski
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Vries Equation ◽  
Wave Theory ◽  
Lagrangian Method ◽  
One Dimensional ◽  
Thin Walls ◽  
De Vries ◽  
Thin Walled

Abstract On the basis of the Lagrangian method a nonlinear wave theory is developed to obtain the Korteweg-de Vries equation for the incompressible, one-dimensional, weak-nonlinear, and dispersive motion of fluid in an infinitely long circular cylinder (with thin walls of elastic rings). This equation has first been obtained by Lamb [1] via the reductive Taniuti-Wei's method [2].

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

The flow of a micropolar liquid layer down an inclined plane

1968 ◽  
Vol 64 (2) ◽  
pp. 513-526 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Thin Films ◽  
Steady State ◽  
Liquid Layer ◽  
Stability Criterion ◽  
Long Waves ◽  
Inclined Plane ◽  
The Stability ◽  
Micropolar Liquid

AbstractConsideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.

The Meniscus Instability of a Thin Liquid Film

1988 ◽  
Vol 55 (4) ◽  
pp. 975-980 ◽  
Author(s):  
H. Koguchi ◽  
M. Okada ◽  
K. Tamura
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Liquid Film ◽  
Tilt Angle ◽  
Stability Criterion ◽  
Thin Liquid Film ◽  
Normal Direction ◽  
Wave Number ◽  
The Stability ◽  
Maximum Amplification

This paper reports on the instability for the meniscus of a thin film of a very viscous liquid between two tilted plates, which are separated at a constant speed with a tilt angle in the normal direction of the plates. The disturbances on the meniscus moving with movement of the plates are examined experimentally and theoretically. The disturbances are started when the velocity of movement of the plates exceeds a critical one. The wavelength of the disturbances is measured by using a VTR. The instability of the meniscus is studied theoretically using the linearized perturbation method. A simple and complete analytical solution yields both a stability criterion and the wave number for a linear thickness geometry. These results compared with experiments for the instability show the validity of the stability criterion and the best agreement is obtained with the wave number of maximum amplification.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

scholarly journals A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 282
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
General Theorem ◽  
Stability Problems ◽  
General Stability ◽  
Stability Theorems ◽  
Additive Type ◽  
The Stability

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

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