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seen Jul 14 at 15:52

Jul
8
comment Ordinary Differential Equations - Sturm Liouville
Hint: Sturm separation theorem
Jul
8
revised How to find out where a solution to a differential equation is defined?
edited tags
Jul
8
comment How to find out where a solution to a differential equation is defined?
Have you read the Picard–Lindelöf theorem?
Jul
8
comment Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
@Vish.Math See the edit. If you find it appropriate, please consider accepting the answer.
Jul
8
revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
Improved the answer to address OP's concerne.
Jul
8
revised Solution of a differentiation in integral form
edited tags
Jul
8
revised Solution of a differentiation in integral form
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Jul
8
comment Solution of a differentiation in integral form
No offence, but it is my impression that you might be reading something more complex than you can handle right now. You really need to step up your knowledge on special functions, separation of variables, eigenfunctions and eigenvalues, Fourier and Laplace transforms, etc. if you want to fully understand the maths that are being used in the articles you are trying to read.
Jul
8
answered Solution of a differentiation in integral form
Jul
5
comment Plotting graphs using numerical/mathematica method
@ComplexGuy In your first plot, you have the wrong code. In the second term inside the root it says 3*2^(1 + 2)*A while it should say 32^(1 + 2)*A.
Jul
5
comment Complex integral - winding number
@MhenniBenghorbal Pretty sure. Robjohn's answer address this.
Jul
5
comment Evaluating decay rate with trigonometric explanation
@ComplexGuy Show[Plot[Evaluate[{A/(1 + 2 t^2/R^4)^(3/4) Cos[Sqrt[2] t + 3/2 ArcTan[(Sqrt[2] t)/R^2]], A/(1 + 2 t^2/R^4)^(3/4), -(A/(1 + 2 t^2/R^4)^(3/4)), A/E} /. {A -> 2, R -> 3}], {t, 0, 12}, PlotStyle -> {Red, {Black, Dashed}, {Black, Dashed}, Blue}, AxesLabel -> {"t", "\[Phi](0,t)"}, ImageSize -> 400], Graphics[{Black, PointSize[0.02], Point[{((E^(4/3) - 1)/2)^(1/2) R^2, A/E}], {Black, Line[{{((E^(4/3) - 1)/2)^(1/2) R^2, 0}, {((E^(4/3) - 1)/2)^(1/2) R^2, A/E}}]}}] /. {A -> 2, R -> 3}]
Jul
5
comment Evaluating decay rate with trigonometric explanation
@ComplexGuy See the edit.
Jul
5
revised Evaluating decay rate with trigonometric explanation
added 696 characters in body
Jul
5
revised Evaluating decay rate with trigonometric explanation
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Jul
5
comment Evaluating decay rate with trigonometric explanation
No. The authors are talking about the envelope of the field. You know that $|\phi| \le A_0/(1 + 2 t^2/R^4)^{3/4}$, so the field will oscillate between these values.
Jul
5
answered Evaluating decay rate with trigonometric explanation
Jul
5
comment combination into an aggregate equation
@ComplexGuy In what context does the superimposition principle is refered? If you mean putting two oscillons together, then my guess is that the approximations should be done with a two-peak like function.
Jul
5
revised combination into an aggregate equation
added 1 characters in body; edited tags
Jul
5
answered combination into an aggregate equation