Advanced Method for Solving the Non-linear Multiparameter Spectral Problems

Despite of the fact that in recent years the non-linear analysis is considered as an advanced method of structural analysis, the basic requirements, which are associated with this method in actual Design Codes, are often vague and declarative without clear comments. The main problems, which must be solved for implementation of the non-linear analysis in practical design, are discussed. It was shown, that currently non-linear analysiscan be considered as an additional tool, which is utilizing for limit states checking in special cases, for example, checking of the structural robustness in accidental design situation.

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Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions

Zeitschrift für Naturforschung A ◽

10.1515/zna-2016-0342 ◽

2017 ◽

Vol 72 (1) ◽

pp. 9-15 ◽

Cited By ~ 2

Author(s):

Lili Feng ◽

Fajun Yu ◽

Li Li

Keyword(s):

Schrödinger Equation ◽

Spectral Problem ◽

Darboux Transformation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Soliton Equations ◽

Spectral Problems ◽

Non Linear ◽

And Mathematics

AbstractStarting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.

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Linear spectral problems, non-linear equations and the δ-method

Inverse Problems ◽

10.1088/0266-5611/5/2/002 ◽

1989 ◽

Vol 5 (2) ◽

pp. 87-130 ◽

Cited By ~ 97

Author(s):

R Beals ◽

R R Coifman

Keyword(s):

Linear Equations ◽

Spectral Problems ◽

Non Linear ◽

Non Linear Equations

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Spectral Problems for Non-Linear Sturm-Liouville Equations with Eigenparameter Dependent Boundary Conditions

Canadian Journal of Mathematics ◽

10.4153/cjm-2000-011-1 ◽

2000 ◽

Vol 52 (2) ◽

pp. 248-264 ◽

Cited By ~ 3

Author(s):

Paul A. Binding ◽

Patrick J. Browne ◽

Bruce A. Watson

Keyword(s):

Boundary Conditions ◽

Liouville Equation ◽

Spectral Problems ◽

Non Linear ◽

Sturm Liouville ◽

Independent Variable

AbstractThe nonlinear Sturm-Liouville equation−(pyʹ)ʹ + qy = λ(1 − f)ry on [0, 1]is considered subject to the boundary conditions(ajλ + bj)y(j) = (cjλ + dj)(pyʹ)(j), j = 0, 1.Here a0 = 0 = c0 and p, r > 0 and q are functions depending on the independent variable x alone, while f depends on x, y and yʹ. Results are given on existence and location of sets of (λ, y) bifurcating from the linearized eigenvalues, and for which y has prescribed oscillation count, and on completeness of the y in an appropriate sense.

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Non-linear Spectral Problems

Theoretical and Mathematical Physics - Operators, Geometry and Quanta ◽

10.1007/978-94-007-0205-9_6 ◽

2011 ◽

pp. 115-124

Author(s):

Dmitri Fursaev ◽

Dmitri Vassilevich

Keyword(s):

Spectral Problems ◽

Non Linear

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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