MathDB3 problems
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Equivalence of the simplest dispersionless modified DKP equations with the full hierarchy
Equivalence conjecture. Following the analogy with the KP and modified KP hierarchies, these two equations are already equivalent to the whole hierarchy given by the bilinear ident…
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Nonexistence of rational Lax pairs for the presented integrable system
Rational Lax-pair nonexistence conjecture. The system $$ has no nontrivial linear or nonlinear Lax pairs written in terms of rational, rather than algebraic, functions.
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Nonlinear degeneracy conjecture for integrable systems with contact Lax pairs
Nonlinear degeneracy conjecture. All -dimensional integrable systems possessing contact Lax pairs are not weakly nonlinear, equivalently, not linearly degenerate.