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Guidelines for Submitting Equations/Solutions to EqArchive

The database contains 327 equations (15 equations are awaiting activation).

Basic requirements

• The material submitted (exact solutions, transformations, equations, and related information) must not be contained in the following sources:
  • Section Exact Solutions at EqWorld
  • Section EqArchive at EqWorld
  • Basic handbooks
• Visitors can submit:
  • Their own new material (a solution, equation, etc.) that has not been published elsewhere before.
  • Their own material already published, with appropriate references.
  • Other author's material, already published, with appropriate references.
• All contributions must be presented in English using LaTeX.
• The contributor will have to specify:
  • His/her name, e-mail address (it will be seen to the author and website administration), country of residence (optionally the city of residence and the place of work); the submission date will appear automatically.
  • If published elsewhere, full reference to the paper or book where the material was published fully or partially.

Rights and obligations of contributors and website administration

• Contributors are allowed to refer to their material published in any other source.
• Contributors can edit their material (at any time) and delete it if desired (by contacting EqWorld administration).
• EqWorld administration does not bear responsibility for accuracy of any submitted material (equations, solutions, transformations).
• EqWorld administration reserves the right (but does not undertake an obligation) to:
  • edit any submitted material;
  • transfer material from one place to another within EqArchive;
  • transfer material from EqArchive to the section Exact Solutions at EqWorld;
  • remove any material that proved to be erroneous or not to comply with the basic requirements (see above).
• Prior to becoming available for viewing, the submitted material must be activated by the administration.

Material submission

• The presentation of material should clear and concise. See the Exact Solutions section at EqWorld for examples of material presentation.
• For ordinary differential equations and integral equations, use y to denote the dependent variable and x to denote the independent one. In systems of ordinary differential equations, the dependent variables should be denoted x, y, and z, while the independent variable should be denoted t.
• Notation for derivatives: y'_x, y''_xx, y'''_xxx, and y⁽ⁿ⁾_x for n>3.
• For partial differential equations, use w for the dependent variable and t, x, y,... for the dependent ones. If there is a single equation, the derivatives should be written using full notation. For systems of partial differential equations, short notation should be used, for example, w_t, w_x, w_xx, w_xy, w⁽ⁿ⁾_x.
• Use a, b, c, k, s, p, and q to denote parameters in the original equations. Use the letters f, g, and h (or F, G, and H) to denote arbitrary functions.
• If a solution is too cumbersome, consider using a transformation that reduces the original equation to a known one (and give a reference where the latter was solved).
• Two first-order ordinary differential equations are considered equivalent if they are linked by a linear transformation, with respect to the unknowns function, of the form y=f(x)y*+g(x), x=h(x*). Consequently, when adding a first-order ordinary differential equation, the contributor should double check whether associated equivalent equations are already present in the Exact Solutions section at EqWorld and in the basic handbooks. Please do not submit equivalent equations to EqArchive.
• In general, infinite series solutions are not accepted. They may be accepted in exceptional cases only if: (i) they are expressible in terms of standard special functions (you should specify how this is done) and (ii) the results apply to a fairly general class of equations involving arbitrary functions.
• If EqArchive already has an equation for which you intend to add a new solution, you should write the equations in the same notation and give links, in the References field, to the other solutions from EqArchive.

The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

Copyright © 2006-2011 Andrei D. Polyanin, Alexei I. Zhurov and Alexander L. Levitin