Pragabhava
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 Jul5 comment Complex integral - winding number @MhenniBenghorbal Pretty sure. Robjohn's answer address this. Jul5 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}] Jul5 comment Evaluating decay rate with trigonometric explanation @ComplexGuy See the edit. Jul5 revised Evaluating decay rate with trigonometric explanation added 696 characters in body Jul5 revised Evaluating decay rate with trigonometric explanation added 6 characters in body Jul5 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. Jul5 answered Evaluating decay rate with trigonometric explanation Jul5 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. Jul5 revised combination into an aggregate equation added 1 characters in body; edited tags Jul5 answered combination into an aggregate equation Jul5 comment Complex integral - winding number This is incorrect, as you are going around the singularity two times. Jul5 comment combination into an aggregate equation This is a completely ill posed question. You are not giving all the information needed to derive the last equation which, by the way, is not correct. What have you done? Where are you stuck? Have you tried something? It looks like a trivial substitution to me. Jul5 comment Solve the following differential equations by converting to Clairaut's form through suitable substitutions. @Vish.Math What book is that? Jul5 revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions. deleted 2 characters in body Jul5 revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions. added 15 characters in body Jul5 revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions. edited tags Jul5 answered Solve the following differential equations by converting to Clairaut's form through suitable substitutions. Jul2 comment Green function Sturm Liouville equation problem … possible duplicate of Small doubt Green's functions Jul2 revised Green function - i need same HELP deleted 4 characters in body Jul2 revised Green function - i need same HELP added 1 characters in body