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A new variant of Fisher indole synthesis involving Bronsted acid-catalyzed hydrohydrazination of unactivated terminal and internal acetylenes with arylhydrazines is reported. The use of polyphosphoric acid alone either as the reaction medium or in the presence of a co-solvent appears to provide the required balance for activating the C–C triple bond towards the nucleophilic attack of the hydrazine moiety without unrepairable reactivity loss of the latter due to competing amino group protonation. Additionally, the formal hydration of acetylenes to the corresponding ketones occurs under the same conditions, making it an alternative approach for generating carbonyl groups from alkynes.

The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampère type equations is given, in which their unusual qualitative features are noted. For the first time, the Lie group analysis of the considered highly nonlinear PDE with three independent variables is carried out. An eleven-parameter transformation is found that preserves the form of the equation. Some one-dimensional reductions allowing to obtain self-similar and other invariant solutions that satisfy ordinary differential equations are described. A large number of new additive, multiplicative, generalized, and functional separable solutions are obtained. Special attention is paid to the construction of exact closed-form solutions, including solutions in elementary functions (in total, more than 30 solutions in elementary functions were obtained). Two-dimensional symmetry and non-symmetry reductions leading to simpler partial differential equations with two independent variables are considered (including stationary Monge–Ampère type equations, linear and nonlinear heat type equations, and nonlinear filtration equations). The obtained results and exact solutions can be used to evaluate the accuracy and analyze the adequacy of numerical methods for solving initial boundary value problems described by highly nonlinear partial differential equations.

Unsteady equations of flat and axisymmetric boundary layers are considered. For the unsteady axisymmetric boundary layer equation, the problem of group classification is solved. It is shown that the kernel of symmetry operators can be extended by no more than four-dimensional Lie algebra. The kernel of symmetry operators of the unsteady flat boundary layer equation is found and it is shown that it can be extended by no more than a five-dimensional Lie algebra. The non-existence of the unsteady analogue of the Stepanov–Mangler transformation is proved.

The β-carboline motif is common in drug discovery and among numerous biologically active natural products. However, its synthetic preparation relies on multistep sequences and heavily depends on the type of substitution required in the core of the desired β-carboline target. Herein, we demonstrate that this structural motif can be accessed with the microwave-assisted electrocyclic cyclization of heterotrienic aci (alkylideneazinic acid) forms of 3-nitrovinylindoles. The reaction can start with 3-nitrovinylindoles themselves under two sets of conditions. The first one involves microwave irradiation of butanolic solutions of 3-nitrovinylindoles, whereas the second one consists of prior Boc protection of indolic nitrogen, where the protecting group cleanly comes off during the course of the reaction. Alternatively, the reaction can start with 3-nitrovinylindoles prepared in situ using various processes. Finally, the reaction may utilize indoles with β-nitrostyrenes, likely involving the intermediacy of spirocyclic oxazolines, which rearrange to similar heterotrienic systems undergoing cyclization to β-carbolines. As part of this study, several natural products, namely, alkaloids norharmane, harmane, and eudistomin N, were synthesized.

The synthesis of novel, highly functionalized 5-hydroxy 3-pyrrolin-2-ones via a two-step procedure involving an addition reaction between KCN and corresponding chalcones, followed by ring condensation of the obtained β-cyano ketones with het(aryl)aldehydes under basic conditions is described. This protocol enables the preparation of various 3,5-di-aryl/heteroaryl-4-benzyl substituted α,β-unsaturated γ-hydroxy butyrolactams, which are subjects of significant interest to synthetic organic and medicinal chemistry.

A novel, low-cost method for the preparation of not easily accessible free 3-aminoindoles has been developed. This approach is based on a well-established reaction between indoles and nitrostyrene in the presence of phosphorous acid, which results in the formation of 4′-phenyl-4′H-spiro[indole-3,5′-isoxazoles]. The latter could be transformed to corresponding aminated indoles by reaction with hydrazine hydrate in good or excellent yields upon microwave-assisted heating.

The Friedel–Crafts reaction of novel 3,5-diarylsubstituted 5-hydroxy-1,5-dihydro-2H-pyrrol-2-ones was used for low cost, one-pot preparation of polycyclic indole derivatives structurally similar to Ergot alkaloids.

A straightforward three-step procedure affording a wide range of novel 7-aryl substituted paullone derivatives was developed. This scaffold is structurally similar to 2-(1H-indol-3-yl)acetamides—promising antitumor agents—hence, could be useful for the development of a new class of anticancer drugs.

Imidazo[1,5-a]pyridines were efficiently prepared via the cyclization of 2-picolylamines with nitroalkanes electrophilically activated in the presence of phosphorous acid in polyphosphoric acid (PPA) medium.

2-Aryl-2-(3-indolyl)acetohydroxamic acids demonstrate promising antitumor activity, but quickly metabolize in vivo via glucuronidation of hydroxamic acid residue. In an attempt to improve their pharmacokinetics, methyl esters were synthesized via a newly developed protocol for chemoselective mono-methylation of hydroxamic acids. The cytotoxicity of these derivatives against the HeLa cell line was evaluated and found to be inferior compared to the parent lead compounds.

Unusual rearrangements were shown to accompany Brønsted acid-assisted peri-annulations of 1H-perimidines with 5-alkynylpyrimidines. These transformations take different routes depending on the nature of acetylene precursor, and lead to the formation of 7-formyl-1,3-diazopyrenes.

The Michael addition reaction between dithiomalondianilide (N,N′-diphenyldithiomalondiamide) and arylmethylidene Meldrum’s acids, accompanied by subsequent heterocyclization, was investigated along with factors affecting the mixture composition of the obtained products. The plausible mechanism includes the formation of stable Michael adducts which, under the studied conditions, undergo further transformations to yield corresponding N-methylmorpholinium 4-aryl-6-oxo-3-(N-phenylthio-carbamoyl)-1,4,5,6-tetrahydropyridin-2-thiolates and their oxidation derivatives, 4,5-dihydro-3H-[1,2]dithiolo[3,4-b]pyridin-6(7H)-ones. The structure of one such product, N-methylmorpholinium 2,2-dimethyl-5-(1-(2-nitrophenyl)-3-(phenylamino)-2-(N-phenylthiocarbamoyl)-3-thioxopropyl)-4-oxo-4H-1,3-dioxin-6-olate, was confirmed via X-ray crystallography.

Microwave-assisted reaction between 2-(3-oxoindolin-2-yl)-2-phenylacetonitriles andbenzene-1,2-diamines leads to the high-yielding formation of the corresponding quinoxalines as sole, easily isolaable products. The featured transformation involves unusual extrusion of phenylacetonitrile molecule and could be performed in a short sequence starting from commonly available indoles and nitroolefins.

The sequential three-component reaction between o-hydroxybenzaldehydes, N-(cyanomethyl)pyridinium salts and a nucleophile towards substituted chromenoimidazopyridines under oxidative conditions has been developed. The employment of Mn(OAc)3·2H2O or KMnO4 as stoichiometric oxidants allowed the use of a wide range of nucleophiles, such as nitromethane, (aza)indoles, pyrroles, phenols, pyrazole, indazole and diethyl malonate. The formation of the target compounds presumably proceeds through a domino Knoevenagel/cyclization/Michael addition/oxidative cyclization reaction sequence.

Reductions make it possible to reduce the solution of a PDE to solving an ODE. The best known are the traveling wave, self-similar and symmetry reductions. Classical and non-classical symmetries are also used to construct reductions, as is the Clarkson–Kruskal direct method. Recently, authors have proposed a method for constructing reductions of PDEs with two independent variables based on the idea of invariance. The proposed method in this work is a modification of the Clarkson–Kruskal direct method and expands the possibilities for its application. The main result of this article consists of a method for constructing reductions that generalizes the previously proposed approach to the case of three independent variables. The proposed method is used to construct reductions of the unsteady axisymmetric boundary layer equation to ODEs and simpler PDEs. All reductions of this equation were obtained.

A highly efficient and expeditious one-pot approach towards 2-(3-oxoindolin-2-yl)acetonitriles was designed, which involves a base-assisted aldol reaction of ortho-nitroacetophenones, followed by hydrocyanation, triggering an unusual reductive cyclization reaction.

3-(1H-Indol-3-yl)benzofuran-2(3H)-ones were efficiently accessed via polyphosphoric acid-mediated condensation of 3-(2-nitrovinyl)-1H-indoles with phenols.

Unusual reactivity of nitroalkanes, involving formation of aci-forms (nitronic acids or nitronates) and their subsequent interaction with carbon-based nucleophiles, is surveyed in this review.

The recently discovered [4+1]-spirocyclization of nitroalkenes to indoles provided a convenient new approach to 2-(1H-indol-2-yl)acetonitriles. However, this reaction was complicated by the formation of inert 3-(2-nitroethyl)-1H-indole byproducts. Herein, we offer a workaround this problem that allows for effective transformation of the unwanted byproducts into acetonitrile target molecules.

Nitroalkanes activated with polyphosphoric acid could serve as efficient electrophiles in reactions with amines and hydrazines, enabling various cascade transformations toward heterocyclic systems. This strategy was developed for an innovative synthetic protocol employing simultaneous or sequential annulation of two different heterocyclic cores, affording [1,2,4]triazolo[4,3-a]quinolines with 1,3,4-oxadiazole substituents.

Nitroalkanes activated with polyphosphoric acid serve as efficient electrophiles in reactions with various nucleophilic amines. Strategically placed second functionality allows for the design of annulation reactions enabling preparation of various heterocycles. This strategy was employed to develop an innovative synthetic approach towards 3,4-dihydroquinazolines from readily available 2-(aminomethyl)anilines.

This paper describes a number of simple but quite effective methods for constructing exact solutions of nonlinear partial differential equations that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (i) simple exact solutions can serve to construct more complex solutions of the equations under consideration and (ii) exact solutions of some equations can serve to construct solutions of other, more complex equations. In particular, we propose a method for constructing complex solutions from simple solutions using translation and scaling. We show that in some cases, rather complex solutions can be obtained by adding one or more terms to simpler solutions. There are situations where nonlinear superposition allows us to construct a complex composite solution using similar simple solutions. We also propose a few methods for constructing complex exact solutions to linear and nonlinear PDEs by introducing complex-valued parameters into simpler solutions. The effectiveness of the methods is illustrated by a large number of specific examples (over 30 in total). These include nonlinear heat equations, reaction–diffusion equations, wave type equations, Klein–Gordon type equations, equations of motion through porous media, hydrodynamic boundary layer equations, equations of motion of a liquid film, equations of gas dynamics, Navier–Stokes equations, and some other PDEs. Apart from exact solutions to ‘ordinary’ partial differential equations, we also describe some exact solutions to more complex nonlinear delay PDEs. Along with the unknown function at the current time, u=u(x,t), these equations contain the same function at a past time, w=u(x,t−τ), where τ>0 is the delay time. Furthermore, we look at nonlinear partial functional-differential equations of the pantograph type, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments, w=u(px,qt), where p and q are scaling parameters. We propose an efficient approach to construct exact solutions to such functional-differential equations. Some new exact solutions of nonlinear pantograph-type PDEs are presented. The methods and examples in this paper are presented according to the principle “from simple to complex”.