# A fundamental equation for solitary wave and dimension analysis [closed]

According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ What I want to do is to get a equation of solitary wave (solition) from the above Lagrangian which will lead for solving many solitary problems like life-time, dimension analysis etc. My confusion is choosing the potential because it may vary and depend on the author's selection. What are the physical constraints on choosing an appropriate potential? Another rather technical expectation is solitary wave is nonlinear equation so how will I write down the equation as 2nd order differential equation with respect to time?

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## closed as too localized by user1504, Waffle's Crazy Peanut, Emilio Pisanty, Michael Brown, Brandon EnrightMay 31 '13 at 2:00

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Related question by OP: physics.stackexchange.com/q/60915/2451 and links therein. –  Qmechanic Apr 16 '13 at 18:23
@Qmechanic I have made the question a bit more conceptual and distinced it from the more conceptual part. I think with my edits, it is now a valid and legitimate question. Can it be reopend? –  Dilaton May 31 '13 at 9:26
@Dilaton This is still a bad question. I don't think small perturbations will salvage it. –  user1504 May 31 '13 at 15:36
@user1504 I dont see why you say it is still a bad question. In addition, in view of the increased dominance of homework and very low-level questions from people who have almost no physics knowledge of their own, it is particularly bad that (technical) questions about slightly more advanced and/or more fundamental topics can never be reopend when they are closed once. –  Dilaton Jun 1 '13 at 11:30
It simply doesn't matter that the question is about sophisticated math, when it simply requests to be given a finished product without any sign the asker has put any effort into the problem to start with or understands the basics of how solitary waves work. –  dmckee Jun 2 '13 at 21:58